Question

erin goes off on a long bike ride, averaging 10 km/h. one hour later her brother alistair starts chasing after her at 16 km/h. how long will it take alistair to catch up to erin? simultaneous equations

Answer 1

By using simultaneous equations and the concept of relative velocity, it is calculated that Alistair will catch up to Erin approximately 1.67 hours after he starts his chase.

Step-by-step explanation:

To solve for the time it will take Alistair to catch up to Erin, we can use simultaneous equations based on the concept of relative velocity. We need to find the point in time at which Erin and Alistair have traveled the same distance, considering Erin has a one-hour head start when Alistair begins his chase.

Let t be the time in hours that Alistair is biking. Erin has been biking for t + 1 hours by that point since she starts one hour earlier. The distance each has traveled can be represented as follows:

• Distance Erin travels: 10 km/h × (t + 1)
• Distance Alistair travels: 16 km/h × t

Since the distances will be the same at the point Alistair catches up, we can set the equations equal to each other:

10(t + 1) = 16t

To find the solution, we distribute and solve for t:

1. 10t + 10 = 16t
2. 10 = 16t - 10t
3. 10 = 6t
4. t = 10/6
5. t = 5/3 hours or approximately 1.67 hours

Therefore, it will take Alistair approximately 1.67 hours to catch up to Erin.