A car travels 400 miles on level terrain in the same amount of time it travels 160 miles on mountainous terrain. If the rate of the car is 30 miles per hour less in mountains than on level ground, find its rate in the mountains.

Time in terrain travel t1 = 400/ y
Time in mountain travel t2 = 160 / x
where
x - speed in mountain
y - speed in terrain
x = y-30

given t1 = t2

(400 / y) = ( 160 / x )
{400 / y} = {160/(y-30)}
400(y-30) = 160y
400y = 160y +12000
140y= 12000
y =12000/240 miles per hour
=50 miles per hour
terrain speed = 50 miles per hour
mountain speed = 50-30 = 20 miles per hour

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