Courtney is traveling 8 mph to a location and 6 mph back. trip is 7 hours in total. what time did she spend at each speed???
d= 8(7-t)
d= 6t
56 -8t = 6t
56 - 8t + 8t = 6t + 8t
56 = 14t
56/14 = 14t/14
t = 4
time going=d/8
time back=d/6
7=d/8+d/6
solve for d first.
multiply both sides by 24
24*7=3d+4d
24=d
now go back to first equations, solve for times.
To find out the time Courtney spent at each speed, we can use a basic formula: Time = Distance / Speed.
Let's assume that the distance to the location is "D" miles. Since she travels at 8 mph to the location, the time taken for this leg of the trip is D / 8 hours.
On the way back, she travels at 6 mph. So the time taken for this leg is D / 6 hours.
According to the problem statement, the total trip took 7 hours. Therefore, we can create the equation:
D / 8 + D / 6 = 7
Now, let's solve the equation to find the value of D, which represents the distance to the location.
Multiply the equation by the least common multiple (LCM) of 8 and 6, which is 24:
3D + 4D = 7 * 24
7D = 168
D = 168 / 7
D = 24
Therefore, the distance to the location is 24 miles.
Now, we can calculate the time Courtney spent at each speed:
Time at 8 mph = Distance / Speed = 24 / 8 = 3 hours.
Time at 6 mph = Distance / Speed = 24 / 6 = 4 hours.
So, Courtney spent 3 hours traveling at 8 mph and 4 hours traveling at 6 mph.