SOLUTION: Darren drives to school in rush hour traffic and averages 21 mph. He returns home in mid-afternoon when there is less traffic and averages 42 mph. What is the distance between his

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Question 1094907: Darren drives to school in rush hour traffic and averages 21 mph. He returns home in mid-afternoon when there is less traffic and averages 42 mph. What is the distance between his home and school if the total traveling time is 1hr30min?
Found 4 solutions by greenestamps, josgarithmetic, josmiceli, MathTherapy:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!

His afternoon speed is exactly twice his morning speed, so the afternoon trip takes exactly half as long as the morning trip.

Since the total driving time was an hour and a half, the morning trip took an hour and the afternoon trip took half an hour.

Using the time and average speed for either the morning or afternoon trip shows the driving distance to be 21 miles:
21%2A1+=+21 or 42%2A0.5+=+21

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
                 SPEED           TIME        DISTANCE
GOING            21              d/21         d
RETURN           42              d/42         d
Total                            1&1/2

d%281%2F21%2B1%2F42%29=1%261%2F2
Solve for d.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = travel time in hrs going to school
+1.5+-+t+ = travel time in hrs going home
Let +d+ = the one-way distance in miles to school
---------------------------------------------
Equation for going to school:
(1) +d+=+21t+
Equation for going home:
(2) +d+=+42%2A%28+1.5+-+t+%29+
----------------------------
Set (1) = (2)
+21t+=+42%2A%28+1.5+-+t+%29+
+21t+=+63+-+42t+
+63t+=+63+
+t+=+1+
---------------------
(1) +d+=+21t+
(1) +d+=+21%2A1+
(1) +d+=+21+
The distance between home and school is 21 miles
----------------------
check:
(2) +d+=+42%2A%28+1.5+-+t+%29+
(2) +d+=+42%2A%28+1.5+-+1+%29+
(2) +d+=+42%2A.5+
(2) +d+=+21+
OK

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Darren drives to school in rush hour traffic and averages 21 mph. He returns home in mid-afternoon when there is less traffic and averages 42 mph. What is the distance between his home and school if the total traveling time is 1hr30min?
Let distance be D

Then time taken to get to school = D%2F21

Time taken to get home = D%2F42

We then get the following TIME equation: matrix%281%2C3%2C+D%2F21+%2B+D%2F42%2C+%22=%22%2C+3%2F2%29

2D + D = 63 ----- Multiplying by LCD, 42

3D = 63

D, or distance = highlight_green%28matrix%281%2C4%2C+63%2F3%2C+%22=%22%2C+21%2C+miles%29%29

How easy was that?