Any help with this one? Those are the equations I have below, yet still cannot seem to figure this one out.
Jessica drove her car at a certain speed for the first 4 hours and increased its speed by 10 miles/hr, for the next two hours. If the total distance traveled by her was 500 miles, find the speeds at which Jessica drove her car at different times.
V1 = D1 / T1
V2 = V1 + 10
T1 = 4
Ttot = T1 + T2 = 6
Dtot= D1+D2 = 500
Vavg = Dtot / Ttot = 83 1/3
What I did was..
[(V1+V2) / 2 ] = Vavg
[((D1/4)+((D1/4)+10))) / 2 ] = Vavg
Solved for D1 then solved for V1 and got 78 1/3. Checked my math and is correct.
Is there any other way to solve this or did they just approximate in the answers?
These are possible answers:
80 and 90 miles/hr respectively
60 and 80 miles/hr respectively
50 and 60 miles/hr respectively
For the first four hours, she drives at an unknown speed, lets call it . So using the formula:
For the next 2 hours she drives at an increased speed. Lets call this . So using the formula:
But is 10 more than .
The total distance travelled is the combination of the distance traveled over the two times segments. We are given the total distance as 500 miles.
Solving for will give you the speed for the first four hours. Then using the fact given about how much the speed is increased, work out which is the speed for the next two hours.