Question

Kapil Dev and Bishan Singh Bedi started running at 8 am with a speed of 40 km/hr and 18 km/hr respectively for Pragati Maidan from the India gate. Bedi completes the whole distance with a uniform speed. After 1 ½ hr, Kapil Dev was stuck in traffic and reduced his speed. In the next 30 minutes, he could cover only 15 km and covered the remaining distance with a speed equal in magnitude to the total time taken by Bedi in hours to cover the entire journey and reached Pragati Maidan at the same time. At what time did both of them reach Pragati Maidan?

Answer 1

@anteater

Answer 2

hi ,after three weeks i saw u in os

Answer 3

Hello :)

Answer 4

Busy summer!

Answer 5

60km -kapil without struck

Answer 6

for 2 hours he can cover only 75 km

Answer 7

Yes, so when he isn't stuck he covers 60 km

Answer 8

I think I need to work it out on paper first :)

Answer 9

and remaining equal to =18*2=36
36+x

Answer 10

That sounds right, but let me double check

Answer 11

75+(40-x)y=36+36*y

Answer 12

y is time ,x is reduced speed

Answer 13

so sorry 75+(40-x)y=36+18*y

Answer 14

That's ok :) I was trying to leave it all in terms of x in my calculations. I am looking at it again!

Answer 15

oh sry still i made a mistake 75+(40-x)y=18*y

Answer 16

That is ok! I think you are on the right track.

Answer 17

75-xy+22y=0

Answer 18

Good! Now we just need to get x in terms of y (or vice versa)

Answer 19

y*(22-x)=-75

Answer 20

i think x=22

Answer 21

So y represents the time it took Bedi to run the race. And x is Dev's reduced speed?

Answer 22

yes

Answer 23

Ok, thanks! Just a moment, please.

Answer 24

k.yw

Answer 25

I think you are on the right track, but let's look at the last part where Dev slows his pace again.

Answer 26

You have the total distance is 18y, where y is the amount of time it takes Bedi to run the race. And since they both started at 8 am and reached the end of the race at the same time, they both have to have been running for y hours total.

Answer 27

yes already 2 hours over for dev

Answer 28

Yes :) Mind if I draw? It makes it easier for me to keep track.

Answer 29

I think it would work out that way, since Bedi runs 18y miles, where y is the number of hours he runs. Then Dev's distance is broken into parts. He runs for 1.5 hours at 40 km/h, then in the next .5 hour he covers 15 km, and then in the remaining time (y - 2 hours) he runs at a reduced speed, x.

Answer 30

And then they tell you that the reduced speed is equal to the total number of hours that Bedi ran. So x = y

Answer 31

they said the distance covered with a speed equal to time taken by bedi so it will be y not y-2.

Answer 32

Yes, but he is running at a rate of y for the length of time y-2

Answer 33

Would you agree that they both ran for y hours total?

Answer 34

Since they both left at the same time and arrived at the same time?

Answer 35

yes

Answer 36

So then, for Dev, the first part of his race he runs for 1.5 hours (at 40 km/h); the second part of the race he runs for .5 hour (and they tell you he covers 15 km during that part). And so, how long must he run in the final part of the race, the part where he is running at a reduced speed?

Answer 37

20y-xy-5=0

Answer 38

So if he runs for a total of y hours, and he has already (as you said) run for 2 hours, the remaining time would be ...

Answer 39

y(20-x)=5

Answer 40

Let me check :)

Answer 41

x=20,y=5

Answer 42

So if Bedi ran for 5 hours, it would be a distance of 90 km (since 18 X 5 = 90)

Answer 43

yes dev will be135

Answer 44

Then, Dev has already covered 75 km. 90 - 75 = 15 km

Answer 45

15 km is the remaining distance, and if Dev covers this at a rate of 5 km/hour, it will take him 3 hours to cover that part of the race. He has already run 2 hours (1.5 + .5 = 2), so then tacking on another 3 hours will mean that he has run 5 hours as well. Good!!!! :D

Answer 46

So ... we now know that they have both run for 5 hours. If they started at 8 am, what time will it be?

Answer 47

1 pm

Answer 48

Yup!

Answer 49

After which they both collapsed of heat stroke.

Answer 50

It occurs to me that there could be an additional "correct" answer to this problem. If they both ran for 15 hours, they would cover a distance of 270 km. In the first part of the race, Dev would cover 60 km, in the second he would cover 15 km, and then in the final part he would cover 15(15-2) or 195 km. So, if they both ran 15 hours they would arrive at 11 pm. But that seems a bit unrealistic for a run! Ultramarathoners :)

A 5-hour run seems more likely.

Answer 51

yupp:)

Answer 52

Just a moment ... going to find out how long the longest ultramarathon has been ...

Answer 53

I guess that would be this one: http://en.wikipedia.org/wiki/Self-Transcendence_3100_Mile_Race

Answer 54

I think your feet might hate you after that!

Answer 55

oh ur telling the race! right:-)

Answer 56

yessssssssssss........................

Answer 57

LOL !

Answer 58

can we do another problem

Answer 59

Sure!

Answer 60

lol

Answer 61

Did you post another problem on the board? I apologize if I have missed it somehow!

Answer 62

yes i tagged it

Answer 63

Oh! Ok ... Just a moment, then!