Question

Cars Overtaking: distance, speed, and time using rational expressions

Sara left Kootenay National Park at 08:00 and drove toward Vancouver at 85 km/h. Allana left the park an hour later and drove along the same route at 100 km/h. At what time did Allana overtake Sara?

Options:
Option 1: 11:30
Option 2: 12:00
Option 3: 12:30
Option 4: 13:00

Answer 1

Allana overtakes Sara at 14:40.

Step-by-step explanation:

To find out when Allana overtakes Sara, we need to determine the time it takes for Allana to catch up with Sara.

Since they both travel along the same route, we can consider the distance between them as a relative distance.

The distance between Sara and Allana is equal to the distance Sara covers in one hour: 85 km.

Now, we can set up an equation to find the time it takes for Allana to catch up with Sara:

D = rt

85(t + 1) = 100t

85t + 85 = 100t

85 = 100t - 85t

85 = 15t

t = 85/15

t = 5.67 hours

Allana catches up with Sara after approximately 5.67 hours.

Since Allana left one hour later than Sara, the total time will be 5.67 + 1 = 6.67 hours.

Therefore, Allana overtakes Sara at 6.67 hours after 08:00.

To convert this into time, we add 6 hours and 40 minutes to 08:00:

08:00 + 6 hours + 40 minutes = 14:40

So, Allana overtakes Sara at 14:40.