SOLUTION: A bus travels from one town to another at a speed of 42mph. If it had gone 14mph faster, it could have made the trip in a half hour less time. How far apart are the towns?

Question 166811: A bus travels from one town to another at a speed of 42mph. If it had gone 14mph faster, it could have made the trip in a half hour less time. How far apart are the towns?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let d=the distance between the towns
time it takes travellinig at 42 mph=d/42
time it would take travelling 14 mph faster=d/56
Now we are told that if the bus travelled 14 mph faster it could have made the trip in 0.5 hr less time, so our equation to solve is:
(d/42)=d/56+0.5 multiply each term by 504
12d=9d+252 subtract 9d from each side
12d-9d=9d-9d+252 collect like terms
3d=252 divide each side by 3
d=84 mi--------------------------------distance between the two towns
CK
84/42=84/56 + 0.5
2=1.5+0.5
2=2

Hope this helps---ptaylor

RELATED QUESTIONS
a car travels from one town to another at a speed of 42mph. if it had gone 6mph faster,... (answered by ankor@dixie-net.com)

Please help A car travels from one town to another at a speed of 42mph. If it had gone (answered by rwm)

A car travels from one town to another at a speed of 32 mph. If it had gone 4 mph faster, (answered by checkley77)

A car travels from one town to another at a speed of 32 mph. If it had gone 4 mph faster, (answered by Fombitz)

A car travels from one town to another at a speed of 32 mph. If it had gone 4 mph... (answered by checkley71)

A car travels from one town to another at a speed of 32mph. If it had gone 4mph faster,... (answered by richwmiller)

A car travels from one town to another at a speed of 32 mph. If it had gone 4 mph faster, (answered by josmiceli,dabanfield)

a car travels from one town to another at a speed of 18mph. if it had gone 18 mph faster, (answered by mananth)

A car travels from one town to another town at a speed of 18mph. If it had gone 18mph... (answered by ankor@dixie-net.com)