SOLUTION: Monica left Montreal driving at 30 km/h. Wendy left 2 h later and traveled the same road at 40 km/h. At what distance from Montreal will Wendy overtake Monica? use linear sy

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Question 1149559: Monica left Montreal driving at 30 km/h. Wendy left 2 h later and traveled the same road at 40 km/h. At what distance from Montreal will Wendy overtake Monica?

use linear systems (substitution, elimination)

Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let distance be +d
Monica’s speed is 30+%28km%2Fh%29
Wendy’s speed is 40+%28km%2Fh%29
Monica’s time t%5B1%5D
Wendy’s time t%5B2%5D
Time difference between Monica and Wendy meeting is 2 hrs, so
t%5B1%5D-t%5B2%5D=2............eq.1
and, since +d=st=> t=d%2Fs, then
t%5B1%5D-t%5B2%5D=d%2Fs%5B1%5D-d%2Fs%5B2%5D...plug in given speed
t%5B1%5D-t%5B2%5D=d%2F30-d%2F40.........eq.2 ...substitute in eq.1

d%2F30+-+d%2F40+=+2
4d%2F120+-+3d%2F120+=+2
d%2F120+=+2
d+=+240 km

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


When Wendy left, Monica had been driving 2 hours at 30 km/h, so she had traveled 60 km.

Monica travels 10 km/h faster than Wendy; since she needs to make up 60 km to overtake Wendy, it will take her 60/10 = 6 hours.

Since she drives at 40 km/h, the distance from Montreal at which Monica overtakes Wendy is 4*60 = 240 miles.