Question

Two cars are driving towards each other from towns that are 150 miles apart. The first car is traveling 45 miles per hour, and the second is traveling 55 miles per hour. If each leaves at 2:15, when will the two cars pass on the road?

Accepted Answer

To solve, refer to the figure.
Let d1 be the distance traveled by the first car and d2 be the distance traveled by the second car.
Since the two cars are 150 miles apart at the start, when they meet, the sum of their distances traveled is 150 miles.
d_1+d_2=150
Then, express the equation in terms of time. Let t be the number of hours that the cars been traveling. The two cars have the same variable t since they start at the same time. Applying the formula
distance =speed *time
the distance traveled by each car expressed in t are
45t + 55t = 150
The left side simplifies to
100t=150
Dividing both sides by 100, it becomes
(100t)/105=150/100
t=1.5
So the value of t is 1.5 hours.  To get the time, express the value of t in hours and minutes. To do so, convert the decimal part to minutes.
t = 1 hr + 0.5 hr
t = 1 hr + 0.5 h * (60 min)/(1hr)
t = 1 hr + 30 min
It is after 1 hour and 30 minutes that the two cars will meet. Since the cars left at 2:15, therefore, they will pass each other at 3:45.

Math

Two cars are driving towards each other from towns that are 150 miles apart. The first car is traveling 45 miles per hour, and the second is traveling 55 miles per hour. If each leaves at 2:15, when will the two cars pass on the road?

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