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 23 the 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.
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To find Paulo's average speed for the trip to Lucban, let's use the formula:
Average Speed = Total Distance / Total Time
Let's denote Paulo's average speed for the trip to Lucban as "x" km/h.
We know that the distance from Tanauan to Lucban is 75 km and the distance from Lucban to Tanauan is also 75 km, as it is a round trip.
Now, let's find the time taken for the trip to Lucban:
Time = Distance / Speed
Time to Lucban = 75 km / x km/h
Since the average speed on the way back to Tanauan was 10 km/h slower than the trip to Lucban, we can say the speed on the return trip was (x - 10) km/h.
Now, let's find the time taken for the return trip:
Time = Distance / Speed
Time back to Tanauan = 75 km / (x - 10) km/h
It is given that the return trip took 2 hours longer than the trip to Lucban. So we can write the equation:
Time back to Tanauan = Time to Lucban + 2 hours
Substituting the values from the calculations above:
75 km / (x - 10) km/h = 75 km / x km/h + 2
Now, we can solve this equation to find the value of x, which represents Paulo's average speed for the trip to Lucban.