# Time, Speed & Distance Practice problems with shortcut tricks

**Example 1**: Ram has a run up of 100 m. if the speed at which he runs at 36 km/hr how much time does he take to complete his run up?

Now first convert speed into m/s

So 36 km/hr= 36 x 5/18= 10m/s

Time = 100/10= 10 sec

**Example 2**: A man cover certain distance at 50 km/hr and returns back to starting point at 60 km/hr then find his average speed?

Average speed= 2 x 50 x 60/(50+60)

=54.54 km/hr

**Example 3**: A boy goes to school at a speed of 3 km/hr and returns to his home at spped of 4 km/hr . If he takes 5 hrs in all then what is distance between his home and school?

Let the distance is x km.

Time=distance/speed

Time taken during first journey= x/3 hr

Time taken during second journey=x/3 hr

Now x/3 +x/2=5 hr

5x=30

X=6 km

**Example 4**: If instead of going at my usual speed of 30 km/hr , I go to office at 40 km/hr then I reach office 10 minutes early. What is distance traveled?

The equation is quite simple and written as

d/30 – d/40=10/60

d=20

**Example 5**: If instead of going at my usual speed ,I go to office at ¾ of usual speed then I reach office 10 minutes late. What is usual time to cover the distance travelled?

Let the usual time is t min

Time taken at ¾ of usual speed= 4t/3 min

Now 4t/3-t-=10

T=30min

**Example 6**: Shaan sees Uma standing at a distance of 200 m from his position. He increased his speed by 50% and hence takes 20 s now to reach her

- If he travels at the original speed how much time he will take?
- What was his original speed?
- What is his new speed?

1.Travelling at 150% of his original speed ie 3/2 times so he should take 2/3 of his original time i.e 20 So original time=30 sec

2.Original speed= 200/30 m/s=> 24km/hr

3. His new speed is 50% more so 24 x1.5=36km/hr

**Example 7**: A, B and C starts swimming a pool simultaneously. To complete 10 laps A takes 10 min, B takes 8 min and C takes 6 min. What is ratio of speed?

Since the distance is same i.e 10 laps for all three. Speed is inversely proportional to time. So ratio of speed

1/10:1/8:1/6=12:15:20

**Example 8**: Ram and shyam decide to meet somewhere between their houses, which is 30 km apart. Ram rides at 4 km/hr and shyam at 6 km/hr simultaneously then at what distance from Shyam’s house they will meet?

Now suppose two meets at a distance o X km from shyam’s house . then time taken by Ram=

(30-x)/4

Similarly time taken by Shyam=X/6

Since both starts simultaneously so time taken should be equal / soling for X we get

X=18KM from Shyam’s house

**Example 9**: A man takes 8 hrs to walk a certain place and ride back. However, he could have gained 2 hrs, if he has covered both ways by riding. How long would he take to walk both ways?

Walking time+ Riding time= 8 hr——(1)

2 x riding time= 8-2= 6hrs——–(2)

2 x walking time= 2×8-6=10 hrs

So both ways walking will take 10 hrs.

**Example 10**. The distance between two stations, Delhi and Amritsar , is 450 km. A train starts at 4 am and moves towards Amritsar at speed of 60 km/hr. Another train starts from Amritsar and moves towards Delhi at speed of 80 km/hr. How far from Delhi two trains will be meeting?

Suppose the train meet at a distance of x m from Delhi. Let the train from Delhi and Amritsar is A and B respectively.

So Time taken by B to cover (450-x) – Time taken by A to cover X = 40/60

450-x/80- x/60= 40/60

7x=1190

X=170

Thus the train meets at a distance of 170 km from Delhi