SOLUTION: Please help me solve this: Clifford "TI" Harris went on a weekend trip. He averaged 35mi/h in the city and 60mi/h on the highway. If the 150mi trip took 3hrs, how much of the time

Question 152566: Please help me solve this: Clifford "TI" Harris went on a weekend trip. He averaged 35mi/h in the city and 60mi/h on the highway. If the 150mi trip took 3hrs, how much of the time was he driving in the city.
Answer by mducky2(62) (Show Source): You can put this solution on YOUR website!

Here are some equations that might help us.
Speed * Time = Distance
Time = Distance/Speed
Speed = Distance/Time

For ease of labeling, let's label time, distance, and speed with variables:
T = time
D = distance
S = speed

Now let's figure out what information the problem gives us.
speed in city = S_c = 35 mph
speed on highway = S_h = 60 mph
total time = T_total = 3 hours
total distance = D_total = 150 miles

It looks like we can use the first equation to help us. The speed times the time on the city equals the distance in the city. The speed times the time on the highway equals the distance on the highway. Adding the two together should give us the total distance:
Speed * Time = Distance
S_c*T_c = D_c
S_h*T_h = D_h
S_cT_c+S_hT_h = D_total
35T_c + 60T_h = 150

Since we know the total time, we can solve for the time in the highway in terms of the time in the city:
T_c + T_h = 3
T_h = 3 - T_c

Plugging back into the original equation:
35t_c + 60(3 - t_c) = 150
35t_c + 180 - 60t_c) = 150
180 - 25T_c = 150
180 - 150 = 25T_c
30 = 25T_c
T_c = 30/25
T_c = 6/5 hrs
T_c = 1 hr and 12 minutes

Clifford "TI" Harris spent 1 hr and 12 minutes driving in the city.

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