Question

Triplets Peter, Reeta and Nikita have two ways for getting home from school each day: cycle on a tandem bike or walk. The bike can carry either one or two riders at a time. Regardless of the number of people pedalling, cycling speed is 5 times walking speed. The triplets always leave school at the same time and always use the same path between school and home, whether walking or cycling. The school is 5km from home and their walking speed is 4 kilometres per hour.

d) On Thursday, it is Reeta's turn to walk. Peter drops Nikita off at a certain point leaving her to walk home, Meanwhile he returns to pick up Reeta and they cycle home together. If all three arrive home at the same time, how far from school are the drop-off ad pick up points.

Answer 1

Pick up point is 1.43 km from the school and drop point is 3.57 km from the school ( to the nearest hundredth).

Explanation:

School <----------- 5 km ---------------> Home

_______ P _______ D _______

x km y km 5-x-y km

_______

y

_________________

5-x km

D is the point where Peter drops off N and P is the pick point x km from the school where Peter picks up R. He travels back y km to pick up R.

We work in times:

Time = distance / speed

The time that R walks from the school to point P is the same as Peter travels the distance (x + 2y) km, so we have

x/5 = (x + 2y)/20

20x = 5x + 10y

15x - 10y = 0 A

The time that N walks home equals the time that Peter travels y + 5 - x km.

So (y + 5 - x)/20 = (5 - x - y)/5

5y + 25 - 5x = 100 - 20x - 20y

15x + 25y = 75

3x + 5y = 15 B

Solving equation A and B

15x - 10y = 0

3x + 5y = 15

Multiply the second equation by 2:

6x + 10y = 30

Adding this to the first equation

21x = 30

x = 30/21 = 1.4285

So 3(1.4285) + 5y = 15

y = 2.1428

Pick up x = 1.43 km

and the drop is 1.43 + 2.14 = 3,57 km from the school