SOLUTION: Each of two cars, whose average rates are in the ratio of 4:5, travels the distance of 160 miles. If the fast car travels 1/2 an hour less than the slow car, find the average rate

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Question 1066151: Each of two cars, whose average rates are in the ratio of 4:5, travels the distance of 160 miles. If the fast car travels 1/2 an hour less than the slow car, find the average rate of each car.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let their speeds = +4x+ and +5x+
Let the time for the slow car = +t+
+t+-+1%2F2+ = the time for the fast car
----------------------------------------
Slow car:
(1) +160+=+4x%2At+
(2) +160+=+5x%2A%28+t+-+1%2F2+%29+
--------------------------------
(1) +t+=+160%2F%284x%29+
(1) +t+=+40%2Fx+
--------------------------
(2) +160+=+5x%2A%28+40%2Fx+-+1%2F2+%29+
(2) +160+=+200+-+%285%2F2%29%2Ax+
(2) +320+=+400+-+5x+
(2) +5x+=+80+
(2) +x+=+16+
-------------------
+4x+=+4%2A16+
+4x+=+64+
and
+5x+=+5%2A16+
+5x+=+80+
-------------------
The slow car's speed is 64 mi/hr
The fast car's speed is 80 mi/hr
--------------------------------
check:
(1) +160+=+4x%2At+
(1) +160+=+64t+
(1) +t+=+2.5+
and
(2) +160+=+5x%2A%28+t+-+1%2F2+%29+
(2) +160+=+80%2A%28+t+-+.5+%29+
(2) +160+=+80t+-+40+
(2) +80t+=+200+
(2) +t+=+2.5+
OK