Year 8 Linear graphs, equations and inequalities — Easy exercise 16

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Two friends, Sam and Jess, start walking from the same point in Sydney. Sam walks at a constant speed of 52 metres per minute, and Jess walks at 22 metres per minute in the same direction.

After how many minutes will the distance between them be exactly 900 metres? Solve algebraically and verify by substitution.

What is the exact number of minutes?

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Illustration: y = x + 1. Each unit right adds one unit up; the y-intercept is 1.

The level beam represents equality, not measured weights. Subtract 6 from both sides of x + 6 = 14 to leave x = 8.

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Worked solution

Sam walks at 52 m/min and Jess at 22 m/min in the same direction, so the relative speed between them is 52 - 22 = 30 m/min.
The distance between them increases at a rate of 30 metres per minute.
Let t be the time in minutes after which the distance between them is 900 metres. The equation is: 30t = 900.
Solve for t by dividing both sides by 30: t = 900 / 30.
900 ÷ 30 = 30. So t = 30 minutes.
Verify by substitution: after 30 minutes, Sam has walked 52 × 30 = 1560 metres.
After 30 minutes, Jess has walked 22 × 30 = 660 metres.
The distance between them is 1560 - 660 = 900 metres, which matches the given distance.
The solution is correct because substitution confirms the distance is exactly 900 metres.

Reference answer: 30 minutes

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