In an automobile race, the rate of one car was 120 mi/hr and the rate of another was 105 mi/hr. If the faster car finished the race 20 minutes before the slower one, what was the distance of the race?
In an automobile race, the rate of one car was 120 mi/hr and the rate of another was 105 mi/hr. If the faster car finished the race 20 minutes before the slower one, what was the distance of the race?
To find the distance of the race, we need to determine the time it took for each car to complete the race.
Let's assume that the time taken by the faster car to finish the race is represented by t hours.
Since the rate of the car is given as 120 mi/hr, we can calculate the distance covered by the faster car using the formula Distance = Rate × Time. Therefore, the distance covered by the faster car is 120t miles.
Now, let's find the time taken by the slower car to finish the race. We know that the rate of the slower car is 105 mi/hr. The slower car finished the race 20 minutes (1/3 of an hour) after the faster car. So, the time taken by the slower car is (t + 1/3) hours.
Since the rate of the slower car is given as 105 mi/hr, we can calculate the distance covered by the slower car using the formula Distance = Rate × Time. Therefore, the distance covered by the slower car is 105(t + 1/3) miles.
We're given that the faster car finished the race 20 minutes (1/3 of an hour) before the slower car, so their distances must be equal. Thus, we can set up the equation: 120t = 105(t + 1/3).
To solve for t, we can distribute the 105 to the terms in the parentheses: 120t = 105t + 35.
Next, we'll subtract 105t from both sides of the equation: 120t - 105t = 35.
Combining like terms: 15t = 35.
Now, divide both sides of the equation by 15: t = 35/15 = 7/3.
So, the time taken by the faster car to complete the race is 7/3 hours, or approximately 2.33 hours.
To find the distance of the race, substitute the value of t into the distance formula for the faster car: Distance = 120t = 120 × (7/3) = 280 miles.
Therefore, the distance of the race is 280 miles.
since distance = speed * time,
120t = 105(t + 1/3)
solve for t, then find the distance