Пример задания Problem Solving с подробными комментариями: ''Friends Part''
Friends Part
Question
Alex and Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 4 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R > 8, which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex?
(A) R – 4
| (B) | R R + 4 |
| (C) | R R – 8 |
| (D) | 8 R – 8 |
(E) R2 – 4
Answer
If we want Brenda's distance to be twice as great as Alex's distance, we can set up the following equation:
2(4T) = R(T – 1), where 4T is Alex's distance (rate Ч time) and R(T – 1) is Brenda's distance (since Brenda has been traveling for one hour less).
If we simplify this equation to isolate the T (which represents Alex's total time), we get:
2(4T) = R(T – 1)
8T = RT – R
R = RT – 8T
R = T(R – 8)
| R R – 8 |
= | T |
This is choice C.
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