Question about time

Question

Simran and Champ are walking at a constant speed, though not the same speed as one another. Simran walks from Point A to Point B, while Champ walks from Point B to Point A. They both leave at sunrise, and cross paths at noon. Simran arrives home at Point B at 4 p.m, whereas Champ arrives at point A at 9 p.m. What time was sunrise? Circle the answer that correctly shows the time: a) 4:00 a.m. b) 5:00 a.m. c) 6:00 a.m. d) 6:30 a.m. e) 9:00 a.m. f) 9:30 a.m.

Answer 1

Let's call the number of hours between sunrise and noon x. So, for example, if sunrise were at 4, then x = 8. This means that the total time Simran spent walking was x hours plus an additional 4 hours after noon (x + 4), and the total time Champ spent walking was x hours plus an additional 9 hours after noon (x + 9).

 

Since Simran and Champ met at noon, we can say that in the x hours between sunrise and noon, their combined walking distance was equivalent to the distance from A to B. This means that the proportion of the walk that Simran did before noon plus the proportion of the walk that Champ did before noon should equal the entire walk. In other words, if Simran spent 4/5 of his x + 4 hours before noon, we would expect Champ to have spent 1/5 of his x + 9 hours before noon, since 4/5 + 1/5 = 1 whole walk.

 

Thus, we can set up an equation using walking times, where x/(x+4) represents the proportion of Simran's walk before noon and x/(x+9) represents the proportion of Champ's walk before noon:

 

x/(x+4) + x/(x+9) = 1

 

Now, multiply both sides by (x+4) and (x+9):

 

x(x+9) + x(x+4) = (x+4)(x+9)

 

Then, solve for x:

 

x² + 9x + x² + 4x = x² + 9x + 4x + 36

2x² + 13x = x² + 13x + 36

x² + 13x = 13x + 36

x² = 36

x = ±6

 

We can ignore -6, since there's no such thing as -6 hours. So, x = 6, which means there were 6 hours between sunrise and noon. That means the correct answer is c) 6:00 a.m.