Number, NAPX-F4-NC28 SA

Question

P,Q,RP, Q, R and SS are towns that lie on a straight train track as shown below.

The distance between PP and QQ is half the distance from PP to SS.

The distance from RR to SS is one-fifth the distance from PP to SS.

The distance from QQ to RR is 21 km.

What is the distance between PP and SS?

Worked Solution

PQ=12PSPQ = \dfrac{1}{2} PS

RS=15PSRS = \dfrac{1}{5} PS

PS=PQ+QR+RSPS = PQ + QR + RS

PS=12PS+21+15PSPS = \dfrac{1}{2}PS + 21 + \dfrac{1}{5}PS

PS=710PS+21PS = \dfrac{7}{10}PS + 21

310PS=21\dfrac{3}{10}PS =21
∴\therefore PS = 21×103\dfrac{21 \times 10}{3}
= {{{correctAnswer0}}} {{{suffix0}}}

Variant 0

DifficultyLevel

733

Question

P,Q,RP, Q, R and SS are towns that lie on a straight train track as shown below.

The distance between PP and QQ is half the distance from PP to SS.

The distance from RR to SS is one-fifth the distance from PP to SS.

The distance from QQ to RR is 21 km.

What is the distance between PP and SS?

Worked Solution

PQ=12PSPQ = \dfrac{1}{2} PS

RS=15PSRS = \dfrac{1}{5} PS

PS=PQ+QR+RSPS = PQ + QR + RS

PS=12PS+21+15PSPS = \dfrac{1}{2}PS + 21 + \dfrac{1}{5}PS

PS=710PS+21PS = \dfrac{7}{10}PS + 21

310PS=21\dfrac{3}{10}PS =21
∴\therefore PS = 21×103\dfrac{21 \times 10}{3}
= 70 km

Question Type

Answer Box

Variables

Variable nameVariable value
correctAnswer0
70
prefix0
suffix0
km

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer070

km

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