Question

Ricky, Sam, and Timothy cycles from Airy Town to Brightvale which was 9km apart. Ricky cycles at a constant x km/h. Sam cycled at y km/h faster than Ricky and took 40 minutes to reach Brightvale. Timothy cycles y km/h slower than Ricky and took 50 minutes to complete the same distance.
By forming 2 equations in x and y, find the speed in which Ricky cycled.

Answer 1

12.15 km /h

Step-by-step explanation:

Step 1 :

Given

Distance between Airy Town to Brightvale  = 9 km

Speed of Ricky = x km/h

Step 2:

Speed taken by Sam = x + y km/h

Time taken by Sam = 40 min = 40/60 hrs = 2/3 hrs

so we have (x+y) 2/3 = 9

Step 3:

Speed taken by Timothy = x - y km / h

Time taken by Timothy = 50 min = 50/60 = 5/6 hrs

= > (x-y) 5/6 = 9

Step 4 :

Solving the 2 equations

(x+y) 2/3 = 9 and (x-y) 5/6 = 9 we have

(2/3)x + 2/3(y) = 9 = > 2x + 2 y = 27

5/6(x) - 5/6(y) = 9 = > 5 x - 5 y = 54

Multiplying the first equation by 5 and the second by 2 we have ,

10 x + 10 y = 135 and 10 x - 10y = 108

Adding both,

20 x = 243 => x = 12.15.

This gives speed of Ricky as 12.15 km /h