SOLUTION: 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?.

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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?.
Found 2 solutions by josmiceli, dabanfield:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
d+=+r%2At
(1) d+=+32t
d+=+%2832+%2B+4%29%2A%28t+-+.5%29
d+=+36%2A%28t+-+.5%29
(2) d+=+36t+-+18
Substitute (1) into (2)
32t+=+36t+-+18
4t+=+18
t+=+4.5 hrs
and, since
d+=+32t
d+=+32%2A4.5
d+=+144 mi

Answer by dabanfield(803) About Me  (Show Source):
You can put this solution on YOUR website!
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