Question

The drive from New Orleans to Memphis is 90 miles shorter than the drive from Memphis to Cincinnati, but 150 miles farther than the drive from Cincinnati to Detroit. If the total highway distance of a New Orleans-Memphis-Cincinnati-Detroit trip is 1,140 miles, find the length of the Cincinnati-Detroit leg of the trip.

Answer 1

Answer:

" The length of the Cincinnati-Detroit leg of the trip is 250 miles. "

Step-by-step Solution:

{ Refer to the attachment for a road map in lines }

Let the drive from Cincinnati to Detroit is X miles and also let the drive from Memphis to Cincinnati is Y miles.

ATQ, the drive from New Orleans to Memphis = X + 150 and also = Y - 90

So X + 150 = Y - 90 (since the distances are same for same road drive)

or, Y = X + 240 ..... (1)

Also given, total highway distance of a New Orleans-Memphis-Cincinnati-Detroit trip is 1,140 miles

Then (X + 150) + Y + X = 1140

or, X + 150 + X + 240 + X = 1140 [ by (1) ]

or, 3X = 750

or, X = 250

Therefore, the length of the Cincinnati-Detroit leg of the trip is 250 miles.