Expert: Scott A Wilson - 1/17/2011

Question
At the beginning of a walk, Rizza and Angel are 30 km apart. If they leave at the same time and walk at the same direction, Rizza overtakes Angel in 6 hours. If they walk towards each other, they meet in 5 hours. What are their speeds?


-Thank you.

Answer
Rita will overtake Angel in 6 hours.  If R is the hourly speed of Rita, Rita will travel 6R in six hours.  If A is the hourly speed of Angel will travel 6A in 6 hours.  Since Angel starts 30 km in the lead, the equation is 6R = 6A + 30.

Since if they walk towards each other they will meet in 5 hours, the distance travelled will be
5A + 5R, and that distance will be 30.  So the whole equation is 5R + 5A = 30.

The 1st equation can have every term divided by 6 to get a value for R.
That should give R = A + 5.

Put this value of R into 5R + 5A = 30 and we should get 5(A+5) + 5A = 30.
Multiplying out the 1st term gives 5A + 25 + 5A = 30.
Adding the terms for A and subtracting 25 from both sides gives 10A = 5.

This means A is only 5/10 = 1/2.
SInce R is travelling 5 km/hr faster, the speed of R is 5 1/2 km/hr.

Using these values, both equations should be checked to make sure they are right.