SOLUTION: Mike drove to a friends house at a rate of 40 miles mph. The return trip he traveled at a rate of 45 mph. Total driving time was 4 hours. What is the distance Mike traveled?

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Mike drove to a friends house at a rate of 40 miles mph. The return trip he traveled at a rate of 45 mph. Total driving time was 4 hours. What is the distance Mike traveled?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 650320: Mike drove to a friends house at a rate of 40 miles mph. The return trip he traveled at a rate of 45 mph. Total driving time was 4 hours. What is the distance Mike traveled?
Found 2 solutions by josmiceli, Alan3354:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = distance to friend's house in miles
Let +t+ = time in hrs to drive to friend's house
given:
To friend's house:
(1) +d+=+40t+
Return trip:
(2) +d+=+45%2A%28+4-t+%29+
-------------------
Substitute (1) into (20
(2) +40t+=+45%2A%28+4-t+%29+
(2) +40t+=+180+-+45t+%29+
(2) +85t+=+180+
(2) +t+=+36%2F17+
(2) +t+=+2.1176+
Plug this result back into (1) or (2)
(1) +d+=+40t+
(1) +d+=+40%2A%28+36%2F17+%29+
(1) +d+=+84.706+
and +2d+=+169.412+
Mike traveled 169.412 mi
check:
(2) +84.706+=+45%2A%28+4-t+%29+
(2) +84.706+=+180+-+45t+
(2) +45t+=+180+-+84.706+
(2) +45t+=+95.294+
(2) +t+=+2.1176+
OK


Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Mike drove to a friends house at a rate of 40 miles mph. The return trip he traveled at a rate of 45 mph. Total driving time was 4 hours. What is the distance Mike traveled?
----------------
Avg speed for the round trip = 2*40*45/(40 + 45)
= 720/17 mi/hr
RT distance = (720/17)*4 = 2880/17 miles