Question

NONE CAN SOLVE!! It takes Lucas 3 hours to cycle from his home to his friend's village. But if he travels 5 mph slower, it will take him 1.5 hours longer. How far is the friend's village from Lucas' house?

Answer 1

It takes Lucas 3 hours to cycle from his home to his friend’s village:

3 hours • (a certain speed) = distance in miles

If he travels 5mph slower, it will take him 1.5 hours longer:

4.5 hours • (the same speed - 5mph) = the same distance in miles

Equation:

4.5 • (x - 5) = 3x

4.5x - 22.5 = 3x

1.5x = 22.5

x (speed) = 15mph

Distance between Lucas’ house and his friend’s village:

3hours • 15mph = 45 miles

OR

4.5hours • (15mph - 5mph) = 45 miles

Answer 2

Using a system of equations, the distance between village and Lucas's house is 45 miles

Recall :

• Distance, d = speed × time

Let initial speed = s

d = 3s - - - - - (1)

d = (3 + 1.5) × (s - 5) - - - (2)

d = 4.5(s - 5)

d = 4.5s - 22.5 - - - - (3)

Equating (1) and (3)

3s = 4.5s - 22.5

Collect like terms

3s - 4.5s = - 22.5

-1.5s = 22.5

s = 15 hours

Hence, the distance is (15 × 3) = 45 miles.

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