Complete Question
A man on a road trip drives a car at different constant speeds over several legs of the trip. He drives for 55.0 min at 60.0 km/h, 18.0 min at 80.0 km/h, and 60.0 min at 60.0 km/h and spends
25.0 min eating lunch and buying gas
What is the total distance traveled over the entire trip (in km)
Answer:
The value is [tex]D = 139.02 \ km[/tex]
Explanation:
From the question we are told that
For [tex] t_1 = 55 min = \frac{55}{60} = 0.917 \ h[/tex] the speed is [tex]v_1 = 60 \ km/h[/tex]
For [tex] t_2 = 18 min = \frac{18}{60} = 0.3 \ h[/tex] the speed is [tex]v_2 = 80 \ km/h[/tex]
For [tex] t_3 = 60 min = \frac{60}{60} = 1 \ h[/tex] the speed is [tex]v_3 = 60\ km/h[/tex]
The time taken to have lunch is [tex]t _l = 25 \ min = \frac{25}{60} = 0.42 \ h[/tex]
Generally the total distance traveled over the entire trip (in km) is mathematically represented as
[tex]D = t_1 * v_1 + t_2 * v_2 + t_3 * v_3[/tex]
=> [tex]D = 0.917 * 60 + 0.3 * 80 + 1 * 60[/tex]
=> [tex]D = 55.02 + 24 + 60[/tex]
=> [tex]D = 139.02 \ km[/tex]
