From two cities that are 500 miles apart, two cars left simultaneously moving towards each other. The speed of one car was 10 mph greater than the speed of the other car. In 5 hours cars met. Find the speed of each car.

Question

05-12-2019
Mathematics

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From two cities that are 500 miles apart, two cars left simultaneously moving towards each other. The speed of one car was 10 mph greater than the speed of the other car. In 5 hours cars met. Find the speed of each car.

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WaywardDelaney WaywardDelaney · Answer 1 · 2019-12-10T17:53:10+01:00

Answer:

The speed of one car is 45 miles per hour

The speed of other car is 55 miles per hour

Step-by-step explanation:

Given as :

The distance between the two cities = 500 miles

The Time at which the two cars meets = 5 hours

The speed of one car was 10 mph greater than the speed of other

Now, let the speed of one car = s mph

So, The speed of the other car = ( 10 + s ) mph

According to question both car moving towards each other

So, The relative speed = s + ( 10 + s )

Since distance = speed × time

Or, 500 miles = [ s + ( 10 + s ) ] × 5

Or, 500 = ( 10 + 2 s ) × 5

Or, 10 + 2 s =[tex]\frac{500}{5}[/tex]

Or, 10 + 2 s = 100

or, 2 s = 100 - 10

Or, 2 s = 90

∴ s = [tex]\frac{90}{2}[/tex]

I.e s = 45 mph

So, the speed of one car = s = 45 mph

The speed of other car = 10 + s = 10 + 45 = 55 mph

Hence The speed of one car is 45 miles per hour

And The speed of other car is 55 miles per hour Answer

raphealnwobi raphealnwobi · Answer 2 · 2021-10-18T12:11:06+02:00

The slower car is 45 mph while the faster car is 55 mph

Speed is the ratio of the distance travelled to the total time taken. Speed is given by:

speed = distance/time

Let a represent the speed of the slower car and b represent the speed of the faster car.

Let d₁ be the distance covered by the slower car and d₂ be the distance covered by the faster car. Since they drove for 5 hours before they met, hence:

For the slower car:

a = d₁/5

d₁ = 5a

For the faster car:

b = d₂/5

d₂ = 5b. But b = a + 10 (10 mph greater), hence:

d₂ = 5(a + 10)

d₂ = 5a + 50

The cities are 500 miles apart, hence:

d₁ + d₂ = 500

5a + 5a + 50 = 500

10a = 450

a = 45 mph

b = a + 10 = 45 + 10 = 55 mph

Therefore the slower car is 45 mph while the faster car is 55 mph

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