2023 AMC 8
Complete problem set with solutions and individual problem pages
Viswam walks half a mile to get to school each day. His route consists of city blocks of equal length and he takes minute to walk each block. Today, after walking blocks, Viswam discovers he has to make a detour, walking blocks of equal length instead of block to reach the next corner. From the time he starts his detour, at what speed, in mph, must he walk, in order to get to school at his usual time?
- A.
- B.
- C.
- D.
- E.
Solution 1
Note that Viswam walks at a constant speed of blocks per hour as he takes minute to walk each block. After walking blocks, he has taken minutes and has minutes remaining to walk blocks. Therefore, he must walk at a speed of blocks per hour to get to school on time, from the time he starts his detour. Since he normally walks mile, which is equal to blocks, mile is equal to blocks. Therefore, he must walk at mph from the time he starts his detour to get to school on time, so the answer is .
Solution 2
Viswam walks blocks, or half a mile, in minutes. Therefore, he walks at a rate of mph. When he takes his detour, he must travel blocks instead of . Our final equation is .
