14. a person drives 100 km to his grandfather's house. on the
way to grandfather's, he drives half the time at 50 km/h and half
the time at 100 km/h. what is the total time of his trip?
a) 80 minutes.
b) 90 minutes.
c) 40 minutes.
d) 60 minutes.
e) 120 minutes.
the answer is a ,but when i solve it i get a. can you me ,

A) 80 minutes

Explanation:

Since both speeds were traveled at for the same time, adding the time spent travelling at each of the speeds is the total time.

let a be the time travelled at one speed

2a = t

To find the time traveled at each speed, write a formula including the distance. The total distance is the sum of the time travelled at each speed.

d = 100km

d = (50km/h)a + (100km/h)a

d = (150km/h)a            Simplified by adding

100km = (150km/h)a       Substitute the total distance for "d"

a = 100km ÷ 150km/h      Isolating "a" to find

a = 2/3h       Time travelled at one speed in hours

Substitute a=2/3h into the total time formula

2a = t

2(2/3)h = t

4/3h = t       Total time of trip in hours

t = 4/3h       Variable on left side for standard formatting

The speeds are 50km/h and 100km/h. Remember the unit for the answer is in hours.

Convert the answer to minutes. There are 60 minutes each hour.

(4/3)h X 60min/h = (240/3)min

= 80min

Therefore the total time of his trip is 80 minutes.

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