<u>Answer-</u>
<em>The distance d across the lake is </em><em>90ft.</em>
<u>Solution-</u>
In the picture,
ΔABC ≈ ΔCDE
Because,
- ∠ACB = ∠DCE (∵ vertical opposite angles)
- ∠B = ∠D = 90°
- ∠ACB = ∠CED (∵ as other two angles are same and sum of those two angles when subtracted from 180° will result the same)
So, from similarity properties
This is an RTD question. Here is a table based on the given information:
up/down . . . .rate . . . .time . . . .distance
upstream . . . . r-4 . . . . T . . . . 7
downstream . . . . r+4 . . . . T . . . .15
Now, rate x time = distance, so
time = distance / rate.
solve each for T and we get
T = (7/(r-4))
T = (15/(r+4))
set the times equal and we get
7%2F%28r-4%29+=+15%2F%28r%2B4%29
cross multiply to get
7r+%2B+28+=+15r+-+60
subtract 7r to get
28+=+8r+-+60
add 60 to both sides to get
88+=+8r
divide by 8 to get
r+=+8
Since 3 out of 8 are cranberry, the fraction is 3/8. In order to convert it, you divide the top number by the bottom, and you get 0.375. In order to get the percent, you would multiply it by 100, and you get 37.5 %
The answer is 37.5%