Question

Willie left the mall and traveled toward the town hall at an average speed of 40 km/h. Gabriella left two hours later and traveled in the opposite direction with an average speed of 70 km/h. Find the number of hours Gabriella needs to travel before they are 410 km apart.

a) 1 hour
b) 3 hours
c) 4 hours
d) 2 hours

Answer 1

b) 3 hours

Explanation:

Given;

speed of Willie , s = 40 km/h

speed of Gabriella, s = 70 km/h

when they are 410 km apart:

Willie's time = t

Gabriella's time = t- 2

2 hours later, the position of Willie = 40t

2 hours later, the position of Gabriella = -70 (t-2) (since he is traveling in opposite direction)

the difference in their positions = 410 km

40t - {-70 (t-2)} = 410

40t -{-70t + 140} = 410

40t + 70t - 140 = 410

110t = 410 + 140

110t = 550

t = 550 / 110

t = 5 hours

Gabriella's time = t- 2

Gabriella's time = 5 - 2 = 3 hours

Thus, Gabriella needs to travel 3 hours before they are 410 km apart.