A passenger car travels 16 mph faster than the commuter bus. If the bus travels 56 miles in the same time it takes the car to travel 84 miles, what is the speed of each vehicle?

speed of commuter bus: 32 km

speed of passenger car  : 48 mph

Step-by-step explanation:

We will use the concept of speed distance and time.

where time = distance / speed

Let the speed of commuter bus be x mph

Given that passenger car travels 16 mph faster than commuter bus.

Speed of passenger car if speed of commuter bus is x mph (x+16)mph

Distance traveled by commuter bus  = 56 miles

Time taken by commuter bus  to travel 56 miles = 56/X   (1)

Distance traveled by passenger car  = 84 miles

Time taken by passenger car to travel 84 miles = 84/(X+16)   (2)

It is given that time taken by both bus and car is same

so equating equation  1 and 2

we have

56/X = 84/(X+16)   (by cross multiplication we have)

=> 56(X+16)  = 84*X

=> 56X + 896 = 84X

=> 896 = 84X - 56 X

=> 896 = 28X

=> X = 896/28 =  32.

Therefore , speed of commuter bus is x mph or 32 km

speed of passenger car  is x+16 mph = (32+16) mph = 48 mph

step-by-step explanation: