Question

After school, Tony biked toward the mountains at a constant rate of 8 mph. An hour later, Terry biked the same route at a constant rate of 12 mph. Let (t) = Length of time Tony had been biking when Terry caught up. Which expression represents how long Terry had been biking when he caught up with Tony?

a) (t+1)
b) (t-1)
c) (1-t)
d) (t/1)

Answer 1

The expression that represents how long Terry had been biking when he caught up with Tony, given that Terry started an hour after Tony, is (t-1). This is because Terry biked for one hour less than Tony to catch up, assuming Tony's biking time is represented by t.

Step-by-step explanation:

The student is asking about a relative motion problem involving two bikers named Tony and Terry who start biking at different times, but along the same route towards the mountains. To determine the expression that represents how long Terry had been biking when he caught up with Tony, we must consider both their speeds and the time difference in their departures.

Tony starts biking at 8 mph and Terry starts biking an hour later at 12 mph. Let (t) represent the length of time Tony had been biking when Terry caught up. Since Terry started biking an hour after Tony, the time Terry had been biking when he caught up would be (t-1) hours because Terry would have been biking for one hour less than Tony.

Therefore, the correct answer is (b) (t-1).