SOLUTION: Margaret drove to a business appointment at 80 mph. Her average speed on the return trip was 70 mph. The return trip took 1/7hr longer because of heavy traffic. How far did she tra

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Question 1109022: Margaret drove to a business appointment at 80 mph. Her average speed on the return trip was 70 mph. The return trip took 1/7hr longer because of heavy traffic. How far did she travel to the​ appointment?
Found 2 solutions by josmiceli, greenestamps:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = the one-way distance
Let +t+ = time in hrs for the trip at +80+ mi/hr
(1) +d+=+80t+
(2) +d+=+70%2A%28+t+%2B+1%2F7+%29+
----------------------------
+80t+=+70%2A%28+t+%2B+1%2F7+%29+
+80t+=+70t+%2B+10+
+10t+=+10+
+t+=+1+
and
(1) +d+=+80%2A1+
The appointment was 80 mi away
----------------------------------
check:
(2) +d+=+70%2A%28+1+%2B+1%2F7+%29+
(2) +d+=+70%2A%28+8%2F7+%29+
(2) +d+=+80+
OK

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


The solution by the other tutor is fine. Here is a different possible approach -- based on the idea that for trips of the same distance, the ratio of speeds is the reciprocal of the ratio of times.

Let x be the time for the trip to the appointment.
The return trip was at a speed 7/8 of the speed going to the appointment; therefore the amount of time required for the return trip was (8/7)x.
We know the return trip took 1/7 hour longer than the trip there:
%288%2F7%29x-x+=+1%2F7
%281%2F7%29x+=+1%2F7
x+=+1

It took her 1 hour to get to the appointment; at 80mph that means the appointment was 80 miles away.