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Maths Time & Distance Test.6

**Quiz Instructions:**

- There will be 20 multiple choice question in this online test.
- Answer of the questions will change randomly each time you start this test.
- Practice this test at least 3 times if you want to secure High Marks.
- At the End of the Test you can see your Test score and Rating.

1 / 20

**A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?**

2 / 20

**Walking at 80% of his usual speed, a man is 10 mins late to his office. Find the usual time taken by hime to reach his office.**

Let his

usual speed be x kmph

usual travel time be t hours

distance to office be d km d=xt d=(0.8x)*[t+(10/60)] xt=0.8xt+(2x/15) Solving,

t=40 minutes

Let his

usual speed be x kmph

usual travel time be t hours

distance to office be d km d=xt d=(0.8x)*[t+(10/60)] xt=0.8xt+(2x/15) Solving,

t=40 minutes

3 / 20

**At 10 a.m. two trains started traveling toward each other from stations 287 miles apart. They passed each other at 1:30 p.m. the same day. If the average speed of the faster train exceeded the average speed of the slower train by 6 miles per hour, which of the following represents the speed of the faster train, in miles per hour?**

Let the speed of the faster train be x miles per hour and

the distance travelled by it when it meets the slower train be y miles. Time taken by the faster train to cover y miles

= Time taken by the slower train to cover (287-y) miles

= 3.5 hours (y/x) = (287-y)/(x-6) = 3.5 Solving, x = 44 miles/hr

Let the speed of the faster train be x miles per hour and

the distance travelled by it when it meets the slower train be y miles. Time taken by the faster train to cover y miles

= Time taken by the slower train to cover (287-y) miles

= 3.5 hours (y/x) = (287-y)/(x-6) = 3.5 Solving, x = 44 miles/hr

4 / 20

**Three towns X, Y, and Z are on a river which flows uniformly. Y is equidistant from X and Z. If a boats man rows from X to Y and back in 10 hours and X to Z in 4 hours, find the ratio of speed of the boats man in still water to the speed of the current.**

X ———— Y ———— Z

If ‘d’ is the distance between X and Y, then ‘d’ is the distance between Y and Z.

Now the total time for the batsman to row from X to Z is 4 hours. Therefore, time to row from X to Y is 2 hours.

Also the time for the boats man to row from X to Y and back is 10 hours. Hence, time required to row from Y to X is 8 hours.

If, a: speed of boats man in still water

b: speed of the river

d/(a + b) = 2; d/(a – b) = 8

2*(a + b) = 8*(a – b)

a + b = 4a – 4b

3a = 5b

a:b = 5:3

X ———— Y ———— Z

If ‘d’ is the distance between X and Y, then ‘d’ is the distance between Y and Z.

Now the total time for the batsman to row from X to Z is 4 hours. Therefore, time to row from X to Y is 2 hours.

Also the time for the boats man to row from X to Y and back is 10 hours. Hence, time required to row from Y to X is 8 hours.

If, a: speed of boats man in still water

b: speed of the river

d/(a + b) = 2; d/(a – b) = 8

2*(a + b) = 8*(a – b)

a + b = 4a – 4b

3a = 5b

a:b = 5:3

5 / 20

**A and B go cycling in the same direction with speeds of 6 km/hr and 12 km/hr. A car from behind passes them in 9 and 10 seconds respectively. What is the speed of the car?**

The relative speed of A and B is 6 km/hr = 1.67 m/s

As the car passes A after 10s, the distance between A and B after 10s (i.e. at 11th second) is the distance covered by car in 1 second.

Therefore, at t = 11, d = 1.67 * 11

d = 18.33 m

v = d/t = 18.33/1 = 18.33m/s

v = 66 km/hr

The relative speed of A and B is 6 km/hr = 1.67 m/s

As the car passes A after 10s, the distance between A and B after 10s (i.e. at 11th second) is the distance covered by car in 1 second.

Therefore, at t = 11, d = 1.67 * 11

d = 18.33 m

v = d/t = 18.33/1 = 18.33m/s

v = 66 km/hr

6 / 20

**A car travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. What is the average speed for the first 320 km of the tour?**

7 / 20

**A man takes 5 hours 45 min in walking to a certain place and riding back. He would have gained 2 hours by riding both ways. The time he would take to walk both ways is_________?**

Given that time taken for riding both ways will be 2 hours lesser than

the time needed for waking one way and riding back

From this, we can understand that

time needed for riding one way = time needed for waking one way – 2 hours

Given that time taken in walking one way and riding back = 5 hours 45 min

Hence The time he would take to walk both ways = 5 hours 45 min + 2 hours = 7 hours 45 min

Given that time taken for riding both ways will be 2 hours lesser than

the time needed for waking one way and riding back

From this, we can understand that

time needed for riding one way = time needed for waking one way – 2 hours

Given that time taken in walking one way and riding back = 5 hours 45 min

Hence The time he would take to walk both ways = 5 hours 45 min + 2 hours = 7 hours 45 min

8 / 20

**In a journey of 24 miles, two thirds of the distance was travelled with a speed of 40 mph and the remaining with 60 mph. How much time did the journey take?**

(2/3)*24=16 miles Time taken to cover the first 16 miles

= (16/40) hours

= 24 minutes Time taken to cover the next 8 miles

= (8/60) hours

= 8 minutes Time taken for the entire journey

= 32 minutes

(2/3)*24=16 miles Time taken to cover the first 16 miles

= (16/40) hours

= 24 minutes Time taken to cover the next 8 miles

= (8/60) hours

= 8 minutes Time taken for the entire journey

= 32 minutes

9 / 20

**A man travels a distance of 2 km by walking at a speed of 6 km/hr. He returns back at a speed of 4 km/hr. What is his average speed?**

Time taken for the forward journey

= 2/6 = (1/3) hrs Time taken for the return journey

= 2/4 = (1/2) hrs Total time = 5/6 hrs Average speed = 4/(5/6) = 24/5 = 4.8kmph

Time taken for the forward journey

= 2/6 = (1/3) hrs Time taken for the return journey

= 2/4 = (1/2) hrs Total time = 5/6 hrs Average speed = 4/(5/6) = 24/5 = 4.8kmph

10 / 20

**A man rows at a speed of 6 km/hr in still water. If the time taken to row a certain distance upstream is 4 times the time taken to row the same distance downstream, what is the speed of the river?**

Let x be the speed of the river.

Ds = (6 + x) km/hr; Us = (6 – x) km/hr

If t hours is the time to row downstream then 4t hours is the time to row upstream.

(6 + x)*t = (6 – x)*4t

6 + x = 24 – 4x

x = 3.6 km/hr

Let x be the speed of the river.

Ds = (6 + x) km/hr; Us = (6 – x) km/hr

If t hours is the time to row downstream then 4t hours is the time to row upstream.

(6 + x)*t = (6 – x)*4t

6 + x = 24 – 4x

x = 3.6 km/hr

11 / 20

**Two trains 140 metres and 120 metres are running in the same direction with speeds 40 kmph and 60 kmph respectively. In what time will the faster train pass the slower one?**

Total distance = addition of length of the two trains = 140 + 120 = 260 metres

As the two trains are travelling in the same direction, their relative speed is:

v = | v1 – v2 | = | 40 – 60 | = 20 km/hr = 20*1000/60 = 1000/3 metres/min

t = 260/ 1000*3

t = 0.78 minutes

Total distance = addition of length of the two trains = 140 + 120 = 260 metres

As the two trains are travelling in the same direction, their relative speed is:

v = | v1 – v2 | = | 40 – 60 | = 20 km/hr = 20*1000/60 = 1000/3 metres/min

t = 260/ 1000*3

t = 0.78 minutes

12 / 20

**Yalmaz can cover a distance of 400 metres in 2 minutes. Rayan can cover 1 km in 300 seconds. Find the ratio of their speeds.**

Rayan’s speed = 1000/300 = 3.33 m/s

Hence Ratio = 1:1

Rayan’s speed = 1000/300 = 3.33 m/s

Hence Ratio = 1:1

13 / 20

**If the ratio of the speeds of A and B to cover a distance of 200 m is 3:4, then the ratio of the time taken to cover the same distance is________?**

If the ratio of the speeds of two objects is a:b, then the time taken by them to cover the same distance is

b:a Hence, the answer is 4:3

If the ratio of the speeds of two objects is a:b, then the time taken by them to cover the same distance is

b:a Hence, the answer is 4:3

14 / 20

**A car can travel 360km with a ¾ full tank. How many km can it travel with a 2/3 full tank?**

With a full tank, it can travel

360*4/3 = 480 km With 2/3 full tank, it can travel

480*2/3 = 320 km

With a full tank, it can travel

360*4/3 = 480 km With 2/3 full tank, it can travel

480*2/3 = 320 km

15 / 20

**A boats man can row in still water at speed of 7 km/hr. It takes 6 hours more to travel the same distance in upstream than in downstream if the speed of the river is 3 km/hr. what is the distance between the two destinations?**

x = 7 km/hr ; y = 3 km/hr

Ds = 10 km/hr ; Us = 4 km/hr

Distance (d) is same. Therefore, if time taken for downstream is t hours, the time for upstream is (t + 6) hours.

10*t = 4*(t + 6)

6t = 24 ; t = 4 hours

d = 10*4 = 40 km

x = 7 km/hr ; y = 3 km/hr

Ds = 10 km/hr ; Us = 4 km/hr

Distance (d) is same. Therefore, if time taken for downstream is t hours, the time for upstream is (t + 6) hours.

10*t = 4*(t + 6)

6t = 24 ; t = 4 hours

d = 10*4 = 40 km

16 / 20

**If Afnan drives at 4/5th of his usual speed to his office, he is 6 minutes late. What is his usual time to reach his office?**

Let t be his usual time to reach his office and v be his usual speed.

v = d/t ……….(d is the distance Afnan travels while going to his office)

vt = d

At v1 = 4v/5 ; t1 = t + 6

4v/5 = d/(t + 6)

4v/5* (t + 6) = d

4v/5* (t + 6) = vt

On solving we get,

t = 24 minutes

Let t be his usual time to reach his office and v be his usual speed.

v = d/t ……….(d is the distance Afnan travels while going to his office)

vt = d

At v1 = 4v/5 ; t1 = t + 6

4v/5 = d/(t + 6)

4v/5* (t + 6) = d

4v/5* (t + 6) = vt

On solving we get,

t = 24 minutes

17 / 20

**Two boys starts from the same place walking at the rate of 5 kmph and 5.5 kmph respectively in the same direction. What time will they take to be 8.5 km apart?**

Relative speed = 5.5 – 5 = .5 kmph (because they walk in the same direction)

distance = 8.5 km

time = distance/speed=8.5/.5=17 hr

Relative speed = 5.5 – 5 = .5 kmph (because they walk in the same direction)

distance = 8.5 km

time = distance/speed=8.5/.5=17 hr

18 / 20

**A cyclist covers a certain distance in 50 minutes at a speed of 24 kmph. To cover the same distance in 40 minutes, he should travel at a speed of__________?**

Distance = 24*50/60 = 20 km New Speed = 20/(40/60)) = 30 kmph

Distance = 24*50/60 = 20 km New Speed = 20/(40/60)) = 30 kmph

19 / 20

**Excluding stoppages, the average speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?**

Due to stoppages, the bus travels only 45 kms in an hour (9 kms less). To cover a distance of 9 km at a speed of 54 kmph, time taken

= 9/54 = 1/6 hrs = 10 mins.

Due to stoppages, the bus travels only 45 kms in an hour (9 kms less). To cover a distance of 9 km at a speed of 54 kmph, time taken

= 9/54 = 1/6 hrs = 10 mins.

20 / 20

**If a boat is rowed downstream for 50 km in 5 hours and upstream for 24 km in 6 hours, what is the speed of the boat and the river?**

If x: speed of boats man in still water

y: speed of the river

Downstream speed (Ds) = x + y

Upstream speed (Us) = x – y

x = (Ds + Us) / 2

y = (Ds – Us) / 2

In the above problem Ds = 10 ; Us = 4

x = (10 + 4) / 2 = 14/2 = 7 km/hr

y = (10 – 4)/2 = 6/2 = 3 km/hr

If x: speed of boats man in still water

y: speed of the river

Downstream speed (Ds) = x + y

Upstream speed (Us) = x – y

x = (Ds + Us) / 2

y = (Ds – Us) / 2

In the above problem Ds = 10 ; Us = 4

x = (10 + 4) / 2 = 14/2 = 7 km/hr

y = (10 – 4)/2 = 6/2 = 3 km/hr