Question

A person takes a trip, driving with a constant speed of 89.5km/h, except for a 22min rest stop. If the person's average speed is 77,8km/h (a.) how much time is spent on the trip and (b.) how far does the person travel?

Need help finding the starting point to this equation

Answer 1

a) distance=speed*time
89.5*x=77.8*(x+22/60)
solve for x
answer is x+22/60 hours

b) 89.5*x km

Answer 2

could you explain how you came to find this equation

Answer 3

distance=speed*time
x represents the time the person was actually travelling without the 22 minute rest
so that's where 89.5*x comes from where 89.5 is the speed, and x is the time in hours

for 77.8*(x+22/60)
77.8 is the speed and x+22/60 is the total time
its the average speed, which counts in the 22 minutes of rest

Answer 4

r*t = d
average speed * time =distance traveled where t, time, includes both traveling and rest time.
77.8 t = d
If there had been no rest stop then the time would have been less than t by 22 minutes
89.5( t-22/60 ) = d
The distance d is the same value for both equations. Solve the following for t:\[\frac{895}{10} \left(t- \frac{22}{60}\right)=\frac{778}{10}t \]\[t=\frac{1969}{702}=2.80484 \text{ hours} \]how far does the person travel?\[\frac{778}{10}*2.80484 = 218.217 \text{ km}\]