What time will car A catch up to car B

Question

Car A left Sydney for Melbourne at 6:00am and travelled at an average speed of 80km/h. At 7:30am car B left Sydney for Melbourne. If car B travels at an average speed of 100km/h, what time will the cars be in the same place?

Answer 1

Hi Millie, set up a table to solve this problem using the equation: D(istance) = R(ate) * T(ime).

The distance traveled by both cars will be the same. Let t represent the time of travel for car B. Then t + 1.5 will represent the time of travel for car A since car A started 1.5 hours before car B.

Car Distance Rate Time

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A * 80 km/h t + 1.5

B * 100 km/h t

Since they both travel the same distance, we can use the following to solve the problem:

D_A = 80 * (t + 1.5)

D_B = 100 * t

D_A = D_B

Or

80 * (t + 1.5) = 100 * t

80t + 120 = 100t

120 = 20t

t = 6

The two cars will be at the same place in six hours.

Time for car A is 6:00 + 7.5 hours, or 1:30 pm.

Time for car B is 7:30 + 6 hours, or 1:30 pm.

Questions?