Paulo drove 75 km from Tanauan, Batangas to Lucban, Quezon to visit his cousins.
His average speed for the trip to Lucban was 10 km/h faster than on his way back to
Tanauan, and as a result, his return trip took 2 hours longer. What is his average
speed for the trip to Lucban? Write the equation that will represent the function.
To solve this problem, let's break it down step by step:
Step 1: Let's assume that Paulo's average speed on his way to Lucban is x km/h.
Step 2: Since his average speed on his way back to Tanauan is 10 km/h slower, then his average speed on the return trip is (x - 10) km/h.
Step 3: Let's calculate the time it took for Paulo to drive from Tanauan to Lucban. The formula to calculate time is:
Time = Distance / Speed
So, the time for the trip to Lucban is 75 km / x km/h.
Step 4: Now, let's calculate the time it took for Paulo to drive back from Lucban to Tanauan. The formula is:
Time = Distance / Speed
So, the time for the return trip is 75 km / (x - 10) km/h.
Step 5: It is given that the return trip took 2 hours longer than the trip to Lucban. So, we can set up the equation:
75 / x = 75 / (x - 10) + 2
This equation represents the relationship between the speed and time of the two trips.
Step 6: To solve the equation, we can first clear the fractions by multiplying both sides of the equation by x(x - 10):
75 * x(x - 10) / x = (75 / (x - 10) + 2) * x(x - 10)
Simplifying this equation will give us the value of x, which represents the average speed for the trip to Lucban.
Now that we have set up the equation, we can solve it by simplifying and solving for x.