If Olivia drove x km at 60 km/h and then twice as far at 80 km/h. In terms of x, how many hours did the trip take? Give the answer in simplest terms
the time for the first trip was x/60 hrs
the time for the second trip was 2x/80
so the total time was x/60 + 2x/80
=10x/240
= x/24 hours
To determine the time it took for Olivia's trip, we need to calculate the time it took for each leg of the journey and then add them together.
1. The first leg of the trip: Olivia drove x km at a speed of 60 km/h. Using the formula time = distance/speed, we can find the time it took for this leg:
time = x km / 60 km/h
2. The second leg of the trip: Olivia drove twice as far as the first leg, so she traveled 2x km at a speed of 80 km/h. Using the same formula as before, we can find the time for this leg:
time = (2x) km / 80 km/h
Now, we add the times together to get the total time for the trip:
Total time = (x/60) + (2x/80)
To simplify this expression, we can find the least common multiple (LCM) of 60 and 80, which is 240. Multiplying the numerator and denominator of the first term by 4, and the numerator and denominator of the second term by 3, we get:
Total time = (4x/240) + (6x/240)
Combining the terms, we have:
Total time = (4x + 6x) / 240
Simplifying further, the total time in simplest terms is:
Total time = 10x / 240
Thus, the answer in terms of x is 10x/240 hours.