SOLUTION: a bicyclist make the trip between two towns in 5.25 hours. A car with an average speed 30 miles faster than the bicycle, makes the same trip in 1.5 hours. How fast is the car going

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: a bicyclist make the trip between two towns in 5.25 hours. A car with an average speed 30 miles faster than the bicycle, makes the same trip in 1.5 hours. How fast is the car going      Log On

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Question 553491: a bicyclist make the trip between two towns in 5.25 hours. A car with an average speed 30 miles faster than the bicycle, makes the same trip in 1.5 hours. How fast is the car going?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed of the bicycle
Let +d+ = the distance between the towns
given:
+s+%2B+30+ = the speed of the car
Equation for bicycle:
(1) +d+=+s%2A5.25+
Equation for the car:
(2) +d+=+%28+s+%2B+30+%29%2A1.5+
---------------------
(2) +d+=+1.5s+%2B+45+
Substitute (1) into (2)
(2) +5.25s+=+1.5s+%2B+45+
(2) +3.75s+=+45+
(2) +s+=+12+
+s+%2B+30+=+42+
The car is going 42 mi/hr
check answer:
(1) +d+=+s%2A5.25+
(1) +d+=+12%2A5.25+
(1) +d+=+63+ mi
and
(2) +d+=+%28+s+%2B+30+%29%2A1.5+
(2) +d+=+42%2A1.5+
(2) +d+=+63+
OK