The summer camps had a field trip from the campus to Fragrance Hill. They traveled at an average speed of 65 km/h in the first 2 hours. After that, traveled at another average speed of 78 km/h. If the distance between the campus and Fragrance Hill is 364 km, what was the total time for the field trip?

Explanation:

They traveled this distance in 2 parts, essentially. Part 1 had an average speed for a certain number of hours, part 2 had an average speed for a certain number of hours, and those 2 parts taken together took them a distance of 364 km. In equation form, that looks like this:

km/hr part 1 + km/hr part 2 = 364 km

Now we need to find each part on the left side of that equation. Part 1 first:

We traveled 65 km/hr for 2 hours, so that took us

and canceling out the hour label, we have that in part 1 we got

65(2) = 130 km. Good. Now onto the second part, where our unknown is.

We traveled 78 km/hr the second part for x hours, so that took us

and canceling out the hour label, we have that in part 2 we got

78x km. Now we can fill in the main equation (the one in bold print)

130 km + 78x km = 364 km and subtracting 130 km from both sides:

78x km = 234 km and dividing by 78 km:

x = 3 hours. Part 2 took 3 hours. Part 1 took 2 hours, so the whole trip took 5 hours.

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