How to calculate the speed of the slower horse in the following question?

Two horses start trotting towards each other, one from A to B and another from B to A. They cross each other after one hour and the first horse reaches B, 5/6 hour before the second horse reaches A. If the distance between A and B is 50 km, what is the speed of the slower horse?
Options are as follows:
1) 30 km/h
2) 15 km/h
3) 20 km/h
4) 25 km/h

1 Answer
Mar 1, 2018

3) 20 km/h

Explanation:

We have two different times and distances related by the same rate. The basic equation is D = RxxT. The first set is the meeting point, which must be at a point 50 - x from one side and x from the other. Thus, the two rate equations are:
D_1 = R_1xx1 and D_2 = R_2xx1
50 - x = R_1 and x = R_2

The second set are the time equations related to the total distance:
50 = R_1xxT_1 and 50 = R_2xxT_2
We also know that T_1 = T_2 - 5/6 or T_2 = T_1 + 5/6

50 = R_2xx (T_1 + 5/6) ; R_2 = 50/(T_1 + 5/6)
50 = R_1xxT_1 ; R_1 = 50/(T_1)
Pick a number from the options to avoid further math manipulations.
For:
R_2 = 20
20 = 50/(T_1 + 5/6) ; 20T_1 + 100/6 = 50
T_1 = (50 - 100/6)/20 = 1.67
50 = R_1xxT_1 ; 50 = R_1xx1.6667
R_1 = 30
Check:
50 - x = R_1 and x = R_2
50 - x = 30 and x = 20
50 - 20 = 30 CORRECT!

For:
R_2 = 30
30 = 50/(T_1 + 5/6) ; 30T_1 + 100/6 = 50
T_1 = (50 - 100/6)/30 = 1.11
50 = R_1xxT_1 ; 50 = R_1xx1.11
R_1 = 45
Check:
50 - x = R_1 and x = R_2
50 - x = 45 and x = 30
50 - 30 != 45 INcorrect!
You can try out the others.