Question

Two cyclists left Agra for Aligarh simultaneously. The first cyclist stopped after 42 min when he was 1 km short of Aligarh and the other one stopped after 52 min when he was 2 km short of Aligarh. If the first cycled as many kilometres as the second, the first one would need 17 min less than the second. Find the distance between Agra and Aligarh

Answer 1

let d be the distance from Agra to Aligarh, v1 be the first cyclist's speed, and v2 be the second cyclist's speed.

The first cyclist took 42 minutes to travel d-1 kilometers, so d-1 = 42*v
The second cyclist took 52 minutes to travel d-2 kilometers, so d-2 = 52*y
The first cyclist needs 17 less minutes to travel the second cyclist's distance, so he took 52-17 minutes and traveled d-2 distance, so d-2 = 35*v
now you have a system of two equations, d-1=42-v and d-2 = 35*v
Should be easy to solve for d from there

Answer 2

sorry I changed the variables halfway through. v1 is v, and v2 is y

Answer 3

d-1=42-v1->1st
d-2=52-v2->2nd
6=v1+v2

Answer 4

srry it is 35 instead of 52

Answer 5

The first cyclist needs 17 less minutes to travel the second cyclist's distance, so you get the equation d-2 = (52-17) * v1. Combine that equation with d-1 = 42*v1 to solve for d. You can ignore the v2 equation because all you need to solve for is d. Sorry for not being clear.
So you just solve
d-2 = 35 * v1
d-1 = 42 * v1

Answer 6

d=3

Answer 7

v1=-1/7

Answer 8

I think you mixed up your signs somewhere, I got v1 = 1/7

Answer 9

right! d=3km?

Answer 10

I get d = 7km and v1 = +1/7

Answer 11

yes u r right.i went wrong