SOLUTION: In a race, the top speed of one car is nine tenths of the top speed of another. After one half hour the faster car is 10 km ahead of the slower car. FInd the rate of each car, assu

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Question 639510: In a race, the top speed of one car is nine tenths of the top speed of another. After one half hour the faster car is 10 km ahead of the slower car. FInd the rate of each car, assuming they started side by side.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I think they are also assuming they are both
going at top speed the whole time
Let +s+ = the speed of the faster car in km/hr
Let +d+ = distance in km the slower car travels in 1/2 hr
Equation for the slower car:
(1) +d+=+%289%2F10%29%2As%2A%281%2F2%29+
Equation for faster car:
(2) +d+%2B+10+=+s%2A%281%2F2%29+
-------------------
Multiply both sides of (1) by 20
(1) +20d+=+9s+
(1) +d+=+%289%2F20%29%2As+
Substitute this into (2)
(2) +%289%2F20%29%2As+%2B+10+=+s%2A%281%2F2%29+
(2) +9s+%2B+200+=+10s+
(2) +s+=+200+
+%289%2F10%29%2As+=+%289%2F10%29%2A200+
+%289%2F10%29%2As+=+180+
----------------
The speed of the faster car is 200 km/hr
The speed of the slower car is 180 km/hr
----------------
check:
(1) +d+=+%289%2F10%29%2As%2A%281%2F2%29+
(1) +d+=+180%2A%281%2F2%29+
(1) +d+=+90+ km
and
(2) +d+%2B+10+=+200%2A%281%2F2%29+
(2) +d+=+100+-+10+
(2) +d+=+90+ km
OK