Answer :
Answer:
Total time taken(T) = 1.1 hour
Distance = 75.68 km
Explanation:
Given:
Average speed = 68.8 km/h
Constant speed = 98.5 km/h
Rest time = 20 min = 20 / 60 = 0.3333 hour
Find:
Total time taken(T)
Total distance (D)
Computation:
Distance = speed × time
D = 68.8 × t.........Eq1
and
D = 98.5 × [t-0.33]
D = 98.5 t - 32.8333.........Eq2
From Eq1 and Eq2
68.8 t = 98.5 t - 32.83333
29.7 t = 32.83333
t = 1.1
Total time taken(T) = 1.1 hour
Distance = speed × time
Distance = 68.8 × 1.1
Distance = 75.68 km
To calculate the travel time and distance, we set up equations with the given average speed and rest time, then solve for the total time and use it to determine the total distance. Upon calculation , we get that (a) time spent on the trip = .77 h (b) How far does the person travels : 75.845 km
To solve this problem, we need to use the formula for average speed, which is total distance divided by total time. Since the average speed and rest time are given, we can find out the travel time and distance.
Part (a): How much time is spent on the trip?
Let t be the total travel time in hours excluding the rest period. We know the person rested for 20 minutes, which is 1/3 of an hour (20/60). So the total time including the rest is t + 1/3. With an average speed of 68.8 km/h over the entire trip, we can set up the equation:
68.8 km/h = Total Distance / (t + 1/3 hours)
Also, for the driving part, the person travels at 98.5 km/h, so the total distance is also:
Total Distance = 98.5 km/h * t
We then equate the two expressions for total distance:
68.8 km/h * (t + 1/3) = 98.5 km/h * t
This equation can be solved for t to find the total time spent driving . Upon calculation that comes out to be : t = 0.77 h = 46.2 minutes.
Part (b): How far does the person travel?
Once we have t , we can plug it back into Total Distance = 98.5 km/h * t to find the total distance traveled that comes out to be = 75.845 km.
