Question
In a bicycle race, Lionel gives Robert a 500 meter advantage.Lionel also agrees to start 15 minutes after Robert. If Lionelbikes at 17 km/h and Robert at 14 km/h, how long will it takeLionel after he starts biking to overtake Robert? The answer is 1 hour and 20 minutes but I'm not sure how toderive a system of equations from this so that I can arrive at thatanswer. Please help me create a system of equations to get to theanswer. In a bicycle race, Lionel gives Robert a 500 meter advantage.Lionel also agrees to start 15 minutes after Robert. If Lionelbikes at 17 km/h and Robert at 14 km/h, how long will it takeLionel after he starts biking to overtake Robert? The answer is 1 hour and 20 minutes but I'm not sure how toderive a system of equations from this so that I can arrive at thatanswer. Please help me create a system of equations to get to theanswer.
Explanation / Answer
Since Robert has a head start, you need to factor that intohis equation, and don't forget about units. 500 meters = .5 km so Robert has .5 km head start AND Lionel gives him 15 mins toget ahead. You need to find out how much distance Robert can go in15 mins. he can ride at 14 km/h, so 15 mins = .25 h 14 km/h * 0.25h = 3.5 km so Robert's equation looks like this: R = .5 km + 3.5 km + 14 t where the t stands for time Lionel's equation looks like this: L = 17 t where t stands for time. Now you can set the equations equal to one another, because atsome point in time, they will both be at the same spot. 17 t = .5 km + 3.5 km + 14 t and solve for t. here you will get 4/3. this is in hours, to better understandit you can multiply it by 60 to get the mins. You will get 80 mins,which is 1 hour and 20 mins.