SOLUTION: Jojo was joining a field trip to Laguna but arrived 30 minutes after the bus had left. His father decided to go after the bus so Jojo could join. Their car traveled the same route
Question 1166884: Jojo was joining a field trip to Laguna but arrived 30 minutes after the bus had left. His father decided to go after the bus so Jojo could join. Their car traveled the same route as the bus at an average speed of 80 km/h. If the bus traveled at 60 km/h, how long will it take the to overtake the bus?
In 30 minutes (1/2 hour), the bus traveling at 60 km/h travels 30km.
The car overtakes the bus at a rate of (80-60) = 20 km/h.
The time required to overtake the bus is (30km)/(20 km/h) = 3/2 hours, or an hour and a half.
ANSWER: An hour and 30 minutes.
CHECK:
The bus will have traveled for 2 hours at 60 km/h, traveling 2*60 = 120km.
The car will have traveled for 1.5 hours at 80 km/h, traveling 1.5*80 = 120km.
If you need a formal algebraic solution, write and solve the equation that the car traveling at 80 km/h for x hours travels the same distance as the bus traveling at 60 km/h for (x plus 1/2) hours:
When the car started, the bus was 0.5 hour * 60 km/h = 30 km ahead.
The approaching speed / (rate) was 80 km/h - 60 km/h = 20 km/h.
The time to catch the bus was = hours = 1 hour and 30 minutes after the car started.