- Andy is as old as Bruce will be when Andy will be twice as old as Bruce was when Andy's age was half the sum of their present age.
- Bruce is as old as Andy was when Bruce was half the age he will be 10 years from now.
Determine the respective present ages of each of Andy and Bruce.
Andy and Bruce are 40 and 30 years old, respectively.
Here is my more verbose than necessary stream of consciousness solution.
First I will insert timestamps into the text after each verb, the present time, T0 being zero.
A and B are their present ages
Andy is (T0) as old as
Bruce will be (T1) when
Andy will be (T2) twice as old as
Bruce was (T3) when Andy's age was (T4, same time as T3) half the sum of their present age.
At T3=T4 , Andy was (A+B)/2
Andy is older and T3 = -(A-B)/2 = (B-A)/2
At time T3, Bruce was B + T4 = B + (B-A)/2 = (3B-A)/2
At T2, Andy will be (3B-A) which is in the future by (3B-A) - A years
So T2 = 3B-2A years in the future
Ah, T2 and T1 are the same time: Bruce will be B + 3B-2A = 4B-2A
So, A = 4B-2A
4B = 3A from the first sentence
Bruce is (T0) as old as Andy was (T5) when Bruce {was (T6)} half the age he will be (T7) 10 years from now.
T7 = 10
At T6 Bruce's age should equal (B+10)/2, T6 = 5-B/2
T5 and T6 are the same time; at which time Andy's age = A+5-B/2
This last number equals B
B = A+5-B/2
3B = 2A+10 from the second sentence
System of equations
4B = 3A
3B = 2A+10
subtracting: B = A-10
4(A-10) = 3A
A = 40
B = 30
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Posted by Larry
on 2023-08-13 15:40:27 |
Solution
