A car and a motorcycle leave at noon from the same location, heading in the same direction. The average speed of the car is 30 mph slower than twice the speed of the motorcycle. In two hours, the car is 20 miles ahead of the motorcycle. Find the speed of both the car and the motorcycle, in miles per hour.

Step-by-step explanation:

1. Let our Motorcycle variable=X

We know that it travels twice the speed so it's 2M

We also know that the car is 30 mph slower

so our equation is : 2x-30

2. As we're finding speed we will be using the equation: speed=distance X time

So: it also says that we need to find the speed after 2 hours

So by adding in 2 this will be: 2(2x-30)

3. The question also stated that it'll be 20mph ahead (car)

So the equation which we can work out now is

2(2x-30)= 2x+20

4. We can find X

2(2x-30)=2x+20 (Multiply out brackets)

4x-60=2M+20 (Subtract 2M as it's less than 4M)

2x-60=20 (Add 60 as we need to find M)

2x=80 (Divide by 2 as 80 is multiple of 2)

x=40 mph

So, x=40 mph

5. Find the speed of the car and motorcycle

Motorcycle: 40 mph

Car: By using 2x-30

Substitute the 40 with the 2

So, 2*40 is 180

180-30 = 50 mph

Hence, the car is 50 mph and the motorcycle speed is 40 mph

Hope this helps!!!

Have a nice day :)

expression #3 is not equivalent. the others are.

step-by-step explanation: