A passenger train's speed is 60 mi/h, and a freight train's speed is 40 mi/h. The passenger train travels the same distance in 1.5 hours less time than the freight train.

How long does each train take to make the trip?

Wow ! Let's see now . . .
Let's say the passenger train takes ' P ' hours for the trip. Then the freight train takes ' P + 1.5 ' hours for the same distance.
The speed of the passenger train is 60, so he covers ' 60P ' miles. The speed of the freight train is 40, to he covers ' 40(p+1.5) ' miles. But the distances are equal !
60P = 40(P + 1.5) . . . . . There's your equation !
Eliminate parentheses on the right side:
60P = 40P + 60
Subtract 40P from each side:
20P = 60
Divide each side by 20 :
P = 3
**The passenger train takes 3 hours , and the **
freight train takes (P+1.5) = 4.5 hours .
Check:
In 3 hours, the passenger train covers (3 x 60) = 180 miles . In 4.5 hours, the freight train covers (4.5 x 40) = 180 miles . It works. yay !

Answered by AL2006 | 2024-06-10

The passenger train takes 3 hours, and the freight train takes 4.5 hours for the trip. Both trains cover the same distance, verifying the solution is correct. This is confirmed by calculating the distances based on their speeds and travel times.
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Answered by AL2006 | 2024-09-05