Jimmy and Yuri travelled from city A to city B. Jimmy's speed for the first 1/3 of the journey, the next 1/3 of the journey and the last 1/3 of the journey are 5 km/h, 4.5 km/h and  4 kn/h respectively. Yuri's speed for the first 1/2 of the journey and the last 1/2  of the journey are 5 km/h and 4 km/h respectively. Given that Jimmy reached 30 seconds earlier than Yuri, find the distance between city A and city B.

Distance=speed×time, so time=distance/speed.

I assume that ⅓ and ½ refer to the distance AB, which we’ll call d km.

If J and Y are the times that Jimmy and Yuri take to go from A to B, the total time it takes Jimmy is:

J=(d/3)/5+(d/3)/4.5+(d/3)/4=(d/3)(1/5+1/4.5+1/4).

J=(d/3)(1/5+2/9+1/4)=(d/3)(36+40+45)/180=121d/540.

Y=(d/2)(1/4+1/5)=9d/40.

The difference in time is Y-J=d(9/40-121/540)=(d/1080)(243-242)=d/1080.

Yuri took 30secs longer to get to B, and 30secs=1/120 hr.

Therefore d/1080=1/120, d=1080/120=9km.

The distance between the cities is 9km.

by Top Rated User (711k points)