Question

In a bicycle race, Lionel gives Robert a 500 m advantage. Also, Lionel agrees to start 15 min 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

To make things easier, you can first change all the numbers to the same unit, e.g. change km->m and h->min. Then set up two equations of the form D=R*T, where in this case, the D is the same for both of them.

Answer 2

(alternatively, if you'd prefer the numbers to be smaller, convert meters to kilometers, and minutes to hours.)

Answer 3

okay i get that but then how do i do the problem?

Answer 4

You need to set up two D=R*T equations for each cyclist and then set the two distances equal to each other since they'll be at the same location.
For example, Robert starts at T=0 at 14km/h, but has a 0.5km head start, so Robert's distance is D-0.5 = 14T.
Lionel has no head start so has to travel the full D at 17km/h, but is delayed 0.25h. His distance is D = 17(T-0.25).

Answer 5

Does that setup make sense? Can you take it from there?

Answer 6

r t = d
Let "t" be the time taken for Lionel to overtake Robert. The total distance that each travels from the start line will be the same. Distance will be measured in km and time in hours. Solve the following for elapsed time t;\[17t= \frac{1}{2}+\frac{1}{4}14+14t\]The LHS is 17*t, the distance Lionel travels.

The RHS is the distance Robert travels. First Robert pedals out 500m or 1/2 km. Then Robert pedals for 15 min, 1/4 hr, at 14 km/hr. Now a clock starts to measure time t, from that point in time when Lionel starts to ride his bike. Robert continues to pedal his bike at 14 km/hr until intercepted by Lionel, 1hr 20min later.