Question

A bus averages 2 miles per hour faster than a motorcycle. If the bus travels 165 miles in the same time it takes the motorcycle to travel 155 miles, then what is the speed of each?

Answer 1

Answer:

The bus travels at 33 miles per hour while the motorcycle travels at 31 miles per hour

Step-by-step explanation:

Represent the bus average speed with x and the motorcycle average speed with y

Given

$x = y + 2$

Distance covered by bus = 165 miles

Distance covered by motorcycle in same time = 155 miles

Required

Determine the speed of each

Average Speed is calculated as;

$Average\ Speed = \frac{Distance}{Time}$

Since the two are measured with the same time, represent time with T

For the bus

$Average\ Speed = \frac{Distance}{Time}$ becomes

$x = \frac{165}{T}$

Make T the subject of formula

$T = \frac{165}{x}$

For the motorcycle

$y = \frac{155}{T}$

Make T the subject of formula

$T = \frac{155}{y}$

Since, T = T; we have that

$\frac{165}{x} = \frac{155}{y}$

Cross Multiply

$165y = 155x$

Substitute $x = y + 2$

$165y = 155(y+2)$

Open Bracket

$165y = 155y - 310$

Collect Like Terms

$165y - 155y = 310$

$10y = 310$

Divide both sides by 10

$y = 31$

Recall that $x = y + 2$

$x = 31 +2$

$x = 33$

Hence;

The bus travels at 33 miles per hour while the motorcycle travels at 31 miles per hour