Question

For the first 30 km, a bicyclist ride at a speed of v km/hr. For the remaining 17 km, he rode at a speed that was 2 km/hr faster than his original speed. What was the time t that he spent on the entire trip? Let t be the time (in hours) and find t if: v=18

Answer 1

The bicyclist spent approximately 2.52 hours on the entire trip when traveling the first 30 km at 18 km/hr, and the remaining 17 km at 20 km/hr.

Step-by-step explanation:

To determine the total time t that the bicyclist spent on the entire trip when the speed v is 18 km/hr, we need to calculate the time taken for each segment of the journey and then sum them up. We are given:

• For the first 30 km, the speed is v km/hr.
• For the remaining 17 km, the speed is v + 2 km/hr (2 km/hr faster than the original speed).

Let's calculate the time for each segment of the trip:

1. Time for the first 30 km: t1 = distance / speed = 30 km / v
2. Time for the remaining 17 km: t2 = distance / speed = 17 km / (v + 2)

Now we plug in the value of v = 18 km/hr:

1. First segment: t1 = 30 km / 18 km/hr = 1.6667 hours
2. Second segment: t2 = 17 km / 20 km/hr = 0.85 hours

Total time spent on the trip: t = t1 + t2 = 1.6667 hours + 0.85 hours = 2.5167 hours, or approximately 2.52 hours.