Thread: Challenging algebra problem

Dear Sir .
I need some help in the below questions .
Thanks very much

1) When Tom came to London, Kathy was as old as Baba and Tom together.
How old was Tom when Kathy was as old as Baba was when Tom came to London?

2)A swimmer was swimming upstream River A. Near the Bridge R he lost
A ball. After swimming 20 min more upstream he noticed his loss and
swam back to find the ball; he reached it near the Bridge S. Find the
velocity of current at River A if the distance between these two bridges
is 2 km. (Ans: 3 km/h).
How far has the swimmer travelled before he turned back to prick uo the ball.
A schematic diagram can be helpful.

Originally Posted by kingman

Dear Sir .
I need some help in the below questions .
Thanks very much

1) When Tom came to London, Kathy was as old as Baba and Tom together.
How old was Tom when Kathy was as old as Baba was when Tom came to London?

Let T, K, and B be the ages of Tom, Kathy, and Baba when Tom came to London. Then K= T+ B.
From that K- B= T. That is, Kathy is T years older than Baba and so "Kathy was as old as Baba was when Tom came to London" T years ago. T years ago, Tom's age was T- T= 0!

2)A swimmer was swimming upstream River A. Near the Bridge R he lost
A ball. After swimming 20 min more upstream he noticed his loss and
swam back to find the ball; he reached it near the Bridge S. Find the
velocity of current at River A if the distance between these two bridges
is 2 km. (Ans: 3 km/h).

Let v be the speed of the river relative to its banks, and let V be the speed of the swimmer relative to the river. The swimmer's speed, relative to the banks of the river, swimming upstream is V- v. The swimmer's speed relative to the banks of the river, swimming downstream is v+ V. All speeds are in km/min. Let T be the time the swimmer swam downstream after the ball. The ball was floating downstream for T+ 20 minutes and so went a distance v(T+ 20)= 2 km. The swimmer went 20(V- v) km upstream and then T(v+ V) km downstream so we have T(v+ V)- 20(V- v)= 2. Tv+ TV- 20V+ 20v= V(T- 20)+ v(T+ 20)= V(T- 20)+ 2= 2km. That is V(T- 20)= 0 so either V= 0 (the swimmer was just floating in the river himself and so was always beside the ball) or T= 20.

How far has the swimmer travelled before he turned back to prick uo the ball.
A schematic diagram can be helpful.

Dear Sir,
thanks very much for the solution but I wonder whether we can solve the problem by looking at relative speed of swimmer with to the current speed. Also I have difficulty in drawing velocity time graph.
thanks