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A backpacker was walking at a speed of 5 km/h towards Mississauga that was

40 km away. He got a ride from a motorist who drove at 25 km/h in the same direction. They arrived at Mississauga 2.5 hours later. How far had the backpacker walked before he took a ride from the motorist?

Verified Answer :

regalmocha17

Answer:

5.625 km

Step-by-step explanation:

We can represent the word problem as a pair of equations (system of equations):

5w + 25d = 40

w + d = 2.5

Where w = hours walked, d = hours driven

We can solve it by first isolating the walk variable.

w = 2.5 - d

Substitute it back in for w.

5(2.5 - d) + 25d = 40

12.5 - 5d + 25d = 40

12.5 + 20d = 40

20d = 27.5

d = 1.375

Now we have our hours driven, plug it in for d and solve for w.

w = 2.5 - 1.375

w = 1.125

Hours walked = 1.125 hours

Multiply it by 5 to obtain the distance that the backpacker had walked prior to getting a ride with a motorist.

1.125 × 5 = 5.625

Thus, the backpacker had walked a distance of 5.625 km before getting a ride.

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