A car travels 90 miles in the same amount of time that a car traveling 10 mph slower travels 60 miles. find the speed of each car

Speed of the first car is 30 mph and that of the second car is 20 mph.

Step-by-step explanation:

Step 1: Let the speed of the first car be x mph. Then the speed of the second car = x - 10 mph. Distance traveled by the second car = 60 miles. Find the time taken by the second car to travel this distance.

Time = Distance/Speed

        = 60/x - 10 (1)

Step 2: Find the time taken by the first car to travel given distance of 90 miles.

Time = 90/x (2)

Step 3: Given that both cars take the same amount of time, equate the 2 equations. (1) = (2)

⇒ 60/x - 10 = 90/x

⇒ 60x = 90(x-10)

⇒ 2x = 3(x - 10)

⇒ 2x = 3x - 30

⇒ -x = -30

∴ x = 30 mph

⇒ x - 10 = 30 - 10 = 20 mph

Exponential function