Rate of speed

Question

A car leaves St Paul Minnesota at 4pm, a bus leaves at 5pm then travels in the same direction as the car, the car is 12mph faster then the bus, at 8pm the vehicles are 100 miles apart, what is the speed of each vehicle.

Answer 1

Hi Joe, this is an application of the D(istance) = R(ate) * T(imes) equation. The way to solve this type of problem is to build a table with the information you know.

 

Let x be the rate of the bus. Then the rate of the car is x + 12.

 

The time is the difference in the starting time of each vehicle and 8 PM.

 

Vehicle    Distance     Rate      Time

----------------------------------------

Car         4(x + 12)   x + 12    4 hr

Bus         3x             x            3 hr

 

We know the vehicles are 100 miles apart at 8 PM.

 

Distance of the car - distance of the bus = 100 miles.

 

4(x + 12) - 3x = 100

 

Clear parenthesis and collect terms:

 

x + 48 = 100

 

Subtract 48 from both sides:

 

x = 52

 

The bus, represented by x, is traveling at a rate of 52 miles per hour.

 

The car, represented by x + 12, is traveling at a rate of 64 miles per hour.

 

Questions?