You are driving to a concert. To arrive on time, you plan to travel at an average speed of 45 miles per hour. For the first two hours of the trip, you travel at 40 miles per hour. How many hours do you have to travel 55 miles per hour to reach on time?

1 hour.

Step-by-step explanation:

Let us say I want to reach the concert in time t (hours).

Case 1: I can reach in time t by going with speed 45 miles per hour.

Case 2: I can reach in time t by going first 2 hours with speed 40 miles per hour and rest (t-2) hours with speed 55 miles per hour.

Distance travelled in case 1 = speed*time = 45*t miles.

Distance travelled in case 2 = speed*time = 40*2 + 55 * (t-2) miles.

Equating the total distance in both the case:

45*t = 80 + 55 * (t-2)

t = 3 hours.

We have to find the time taken to travel with speed 55 miles per hour

and that is (t-2) = 1 hour.