SOLUTION: Two cars start together and travel in the same direction. One car travels twice as fast as the other. After five hours, they are 275 km apart. How fast is each car traveling?

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Question 763497: Two cars start together and travel in the same direction. One car travels twice as fast as the other. After five hours, they are 275 km apart. How fast is each car traveling?
Found 2 solutions by josmiceli, MathLover1:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed of the slower car in km/hr
+2s+ = the speed of the faster car in km/hr
Let +d+ = the distance in km the slower car travels in 5 hrs
+d+%2B+275+ = the distance in km the faster car travels in 5 hrs
------------------
Slower car:
(1) +d+=+s%2A5+
Faster car:
(2) +d+%2B+275+=+2s%2A5+
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(2) +d+%2B+275+=+10s+
Substitute (1) into (2)
(2) +5s+%2B+275+=+10s+
(2) +5s+=+275+
(2) +s+=+55+
+2s+=+110+
The slower car travels at 55 km/hr
The faster car travels at 110 km/hr
check:
(1) +d+=+s%2A5+
(1) +d+=+5%2A55+
(1) +d+=+275+
and
(2) +d+%2B+275+=+2s%2A5+
(2) +d+%2B+275+=+2%2A55%2A5+
(2) +d+=+550+-+275+
(2) +d+=+275+
OK

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

This is a rate/time/distance problem so we will use the following formula:
Rate+%2A+Time+=+Distance
Establish your terms:
Let r+ be the rate of speed of car A
Let 2r be the rate of speed of car
Let 5r%7D%7D+be+the+distance+car+%7B%7B%7BA travels after 5 hours
Let 5%282r%29+=+10r be the distance car B travels after 5 hours
Since car B is the faster car it will have travelled farther after 5 hours so:
Distance car B travels - distance car A travels is equal to 275
Using our terms from above:
10r+-+5r+=+275
5r+=+275
r+=+55+kph
and
2r+=+110+kph
Car A is travelling at 55kph and car B is tavelling at 110kph.