Problem Solving

Mikrislac wrote: ↑

Tue Aug 11, 2020 4:55 pm

Mona travels from town D to town A at a constant speed of 60 km/hr and from town A to town J at a constant speed of 80 km/hr. She calculates her overall average speed in going from towns D to J via A to be 65 km/hr. What is the ratio of the distances "D to A" and "A to J"?

(A) 2 : 3

(B) 5 : 8

(C) 9 : 20

(D) 12: 13

(E) 22 : 27

Solution:

We can let the distance from D to A be 60 and the distance from A to J be x. We can create the equation:

Total Distance/Total Time = Average Rate

(60 + x) / (60/60 + x/80) = 65

(60 + x) / (1 + x/80) = 65

60 + x = 65(1 + x/80)

60 + x = 65 + 13x/16

3x/16 = 5

x = 80/3

Therefore, the ratio of the distances from D to A to that from A to J is:

60/(80/3) = 60 * 3/80 = 180/80 = 9/4

Answer: None