Word Problem Help

Question

In a bicycle race, Lionel gives gives Robert a 500 m advantage. Also, Lionel agrees to start 15 minutes after Robert. If Lionel bikes at 17 km/h and Robert at 14 km/h, how long will it take Lionel after he starts biking to overtake Robert?

Answer 1

The first thing we need to do is to figure out how far ahead Robert will be when Lionel starts the race.

 

We know that at time t = 0, Robert is already 500m ahead. If Robert bikes at 14 km/h, and he rides for 15 minutes before Lionel even starts, then we can figure out how much distance is between them when Lionel starts:

 

500m = 0.5 km

15 minutes = 0.25h

 

Distance between riders when Lionel starts = 0.5km + 14km/h * 0.25h = 4km

 

Now we know the difference between their speeds is 3km/h when Lionel starts, so we basically need to figure out how long it takes Lionel to go 4km if he's gaining at 3km/h.

 

Therefore:

 

3(km/h) * t(h) = 4(km)

t(h) = 4/3

t = 1.3333333 hours = 1 hour 20 minutes