Bill started west on road U.S. 50, riding a bicycle at an average rate of 9 mph. Four hours later Charles started after Bill on a motor cycle and overtook him in 2 hours. What was Charles' rate?
Which equation could be used to solve for Charles' rate if it is represented by x?
2x = 36
2x = 54
6x = 54
Let's use the equation d = rt, where d is the distance, r is the rate, and t is the time.
Bill traveled for 4 hours at a rate of 9 mph, so the distance he traveled is d = 9 * 4 = 36 miles.
Charles overtook Bill in 2 hours, so the distance Charles traveled is also 36 miles.
Now, let's use the equation d = rt for Charles.
36 = x * 2
Dividing both sides of the equation by 2, we get:
18 = x
Therefore, Charles' rate is 18 mph.
So, the equation that could be used to solve for Charles' rate represented by x is 2x = 36.
To solve this problem, we can set up a distance equation.
Let's denote the distance traveled by Bill as D. Since Bill rode for 4 hours at a rate of 9 mph, his distance is given by D = 9 * 4 = 36 miles.
Charles started 4 hours later and took 2 hours to overtake Bill. Let's denote Charles' rate as x mph. So, Charles' distance is given by D = x * 2 = 2x miles.
Since Charles overtook Bill, their distances must be equal. Therefore, we have the equation:
2x = 36
So, the correct equation to solve for Charles' rate is 2x = 36.
To solve this problem, we can first find the distance that Bill traveled using the formula: distance = rate * time.
Bill rode for 4 hours at an average rate of 9 mph, so the distance Bill traveled is: distance = 9 mph * 4 hours = 36 miles.
Since Charles overtakes Bill, it means that Charles traveled the same distance (36 miles) in 2 hours.
To find Charles' rate, we can use the equation: rate = distance / time.
In this case, the distance is 36 miles and the time is 2 hours. Therefore, the equation is: rate = 36 miles / 2 hours = 18 mph.
So Charles' rate, represented by x in the equations you provided, is 18 mph.
Therefore, none of the equations given would solve for Charles' rate correctly.