Expert: Lynn Houston - 5/13/2010

Question
A car travels with uniform speed. If it would have faster 10 km/h, It would reach destination 2 hours early and if it would have slower 10km/h it would reach destination 3 hours late. What is the distance covered by car.

Answer
rate = r kph ; time = h hours ; distance = rh miles
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Slower speed DATA:
rate = r-10 kph ; time = h+3 hrs ; distance = (r-10)(h+3) miles
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Faster speed DATA:
rate = r+10 kph ; time = h-2 hrs ; distance = (r+10)(h-2) miles
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Equations:
(r-10)(h+3) = rh
(r+10)(h-2) = rh
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rh +3r - 10h - 30 = rh
rh -2r + 10h - 20 = rh
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3r - 10h = 30
-2r+ 10h = 20
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Add to get: r = 50 mph
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Slower speed = r-10 = 40 kph
Faster speed = r+10 = 60 kph

rh = 50h
rh= 40(h+3)

50h = 40h + 120
10h = 120
h = 12

FINALLY!
50(12) = 600 km