Question

The distance from P to Q is four times the distance from Q to R. The distance from p to r is 120 metres. What is the distance from Q to R?

Answer 1

|----------------------------------120 m ------------------------------|

|--------------|--------------|--------------|--------------|--------------|
P Q R

Distance from P to R = 120m

120 ÷ 5 = 24m

The distance from Q to R is 24m.

Answer 2

Let distance from Q to R equal x. Then distance from P to Q is 4x. So we have something like this:

P-------------Q-----R
4x x

Distance all the way from P to R is 4x + x = 5x, and this must be equal to 120. So set up the equation:


`5x=120`

Divide both sides by 5 to isolate x:


`x= 24`

This is the length of QR.

Check to be sure:

P-------------Q-----R
4(24) + 24
96 + 24 = 120

Works!