Ray C. answered • 09/10/19
Stanford Grad with 18 yrs of Algebra Teaching and Tutoring Experience
Bailey,
You asked –
A blue car is traveling toward a city at 65 miles per hour the blue car is 300 miles away a red car is traveling away from the city at 56 miles per hour how long until they meet and how many miles from the city
Answer:
For this word problem, it is a rate * time = distance type of problem. It is important to draw a picture.
Blueà65 mph t 56 mph ßRed
|-----------------300-d-----------|------------d---------------|
Let’s write an equation for the blue car; it is going 65 mph toward the city and it is 300 miles from the city.
65*t = 300-d; rate * time = distance, where t is the variable for time and d is the distance where the cars meet as measured from the city center
Now let’s write an equation from the red car. The difference here is that we only know that is travel 56 mph and it goes away from the city on the same road.
56*t=d; rate * time = distance, where t is the variable for time and d is the variable for distance
Now here is the trick, when the two cars meet, they will have traveled the same amount of time. Knowing that information we can take the red car equation and solve for time.
56*t = d; red car equation
56*t/56 = d/56; divide by 56 on both sides to isolate the variable t
T=d/56
Now plug that answer for t into the blue car equation
65*d/56=300-d; blue car equation
65*d/56 + d = 300 – d+d; isolate the variable d to one side of the equation by adding d to both sides
(65+56)/56 * d = 300; use the distributive property
121/56*d = 300; simplify
d = 300*56/121; divide each side by 121/56 to isolate d
d = 138.84 miles (rounded)
using the red car equation, we can now find the time.
T = d/56 = 138.84/56
T = 2.48 hours.
Now let’s check our answer in the blue car equation
65*2.48 = 300-138.84; substitute d and t into the blue car equation
161.16 = 161.16; this is true, so my answer is correct
Regards,
Ray
