# Car and motorcyclist

A car and a motorcyclist rode against each other from a distance of 190 km. The car drove 10km/h higher than the motorcyclist and started half an hour later. It met a motorcyclist in an hour and thirty minutes. Determine their speeds.

a =  60 km/h
b =  50 km/h

## Step-by-step explanation:

190 = a·(1+30/60) + b·(1+30/60+30/60)
a = 10 + b

90a+120b = 11400
a-b = 10

Row 2 - 1/90 · Row 1 → Row 2
90a+120b = 11400
-2.33b = -116.67

b = -116.66666667/-2.33333333 = 50
a = 11400-120b/90 = 11400-120 · 50/90 = 60

a = 60
b = 50

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