Question 152566
<br>Here are some equations that might help us.
Speed * Time = Distance
Time = Distance/Speed
Speed = Distance/Time
<br>For ease of labeling, let's label time, distance, and speed with variables:
T = time
D = distance
S = speed
<br>Now let's figure out what information the problem gives us.
speed in city = S<sub>c</sub> = 35 mph
speed on highway = S<sub>h</sub> = 60 mph
total time = T<sub>total</sub> = 3 hours
total distance = D<sub>total</sub> = 150 miles
<br>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<sub>c</sub>*T<sub>c</sub> = D<sub>c</sub>
S<sub>h</sub>*T<sub>h</sub> = D<sub>h</sub>
S<sub>c</sub>T<sub>c</sub>+S<sub>h</sub>T<sub>h</sub> = D<sub>total</sub>
35T<sub>c</sub> + 60T<sub>h</sub> = 150
<br>Since we know the total time, we can solve for the time in the highway in terms of the time in the city:
T<sub>c</sub> + T<sub>h</sub> = 3
T<sub>h</sub> = 3 - T<sub>c</sub>
<br>Plugging back into the original equation:
35t<sub>c</sub> + 60(3 - t<sub>c</sub>) = 150
35t<sub>c</sub> + 180 - 60t<sub>c</sub>) = 150
180 - 25T<sub>c</sub> = 150
180 - 150 = 25T<sub>c</sub>
30 = 25T<sub>c</sub>
T<sub>c</sub> = 30/25
T<sub>c</sub> = 6/5 hrs
T<sub>c</sub> = 1 hr and 12 minutes
<br>Clifford "TI" Harris spent 1 hr and 12 minutes driving in the city.