Question 274940
 A car travels from one town to another at a speed of 32 mph. If it had gone 4 mph faster, it could have made the trip in 1/2 hr less time. How far apart are the towns?.

If the distance between towns is d and the time needed to travel at 32 mph is t then we have:

    d = 32*t or
1.) t = d/32

At the faster speed (32+4=36) it takes .5 hours less to travel the same distance so we have:

    d = 36*(t - 1/2) or
2.) d = 36*t - 18

From 1.) we know that t = d/32 so we can substitute d/32 for t in equation 2.) which gives us:

d = 36*(d/32) - 18
d = (36/32)*d - 18
d = (9/8)*d - 18
(9/8)*d - d = 18
d/8 = 18
d = 18*8 = 144