Start by writing how far each vehicle travels in their own directions.
G
Practice makes perfect
We want to find the speed of a train x that leaves a city traveling due to north. At the same time, a car leaves the city traveling due west with a speed that is 15 miles per hour faster than the train, x+15. Knowing this, let's first examine the directions and the corresponding speeds of the vehicles.
After 2 hours later, the distance between the vehicles will be 150 miles. Now we will express how far each vehicle travels at their own directions. To do so, let's multiply their speeds by 2.
Speed
Time
Speed * Time = Distance
Distance
Train
x
2
x * 2
2x
Car
x+15
2
( x+15)* 2
2x+30
Great! Next, let's see the corresponding distances on the diagram.
Notice that we form a right triangle with these three distances. Therefore, we can apply the Pythagorean Theorem to find x.
a^2 + b^2 = c^2
Let's substitute a= 2x, b= 2x+30, and c= 150 into the formula and solve it for x.
Last we can use the Zero Product Property to solve the equation.
x+60=0 ⇔ & x= -60
x-45=0 ⇔ & x= 45
Note that a negative speed does not make sense in our case. Therefore, the speed of the train is 45 miles per hour, which corresponds to option G.
