Liana's class was going on a very exciting school trip, but when Liana got to school, the school bus had already left! Frantic, Liana begged her mom to drive her to catch up with the bus. Liana's mother has to decide quickly whether she can do it. These are the facts to consider: The bus left at 8:00 AM and is moving with the average speed 45 mph. Liana and her mom can leave no earlier than at 8:40. If Liana's mother drives with the average speed 60 mph, when can they catch up with the bus?

They can catch up with the bus at 10:40 am.

Explanation:

1. Set the time when Liana and her mother can leave (8:40 am) as t₀ = 0; thus the time of driving for them will be t.

2. The average speed at whic Liana's mother drive: 60 miles/hour

3. Thus, the distance they will have driven will be:

distance = average speed * time = 60t

4. The time the bus left was 8:00 am, which is 40 minutes before Liana and her mom can leave.

Thus, the time wil have driven when Liana and her mom have driven t hours minutes will be: t + 40 min / 60 min / hour = t + 2/3

5. The average speed of teh bus is 45 miles / hour

6. The distance the bus will have driven will be:

distance = average speed * time = 45 (t + 2/3)

7. When Liana and her mother catch up with the bus, the distances driven by both of them are equal:

60t = 45 (t + 2/3) 60t = 45t + 30 60t - 45t = 30 15t = 30 t = 30/15 = 2

Thus, Liana and her mom can catch up with the bus after 2 hours, since 8:40 am; this is, 10:40 am.