AAPL wrote: ↑

Sat Apr 17, 2021 4:55 pm

E-GMAT

A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and the rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?

A. 2.91 m
B. 3 m
C. 5.82 m
D. 6 m
E. None of these

OA B

Solution:

Since the total area of the park (lawn and crossroads) is 60 x 40 = 2400 sq. m and the area of the lawn is 2109 sq. m, the area of the two crossroads is 2400 - 2109 = 291 sq. m.

Let’s let w = the width of each crossroad. Now, note that one road will be 40 meters long and x meters wide, or 40w, and the other road will be 60 meters long and w meters wide, or 60w. Also note that the area where the two roads cross each other (overlap) has been double counted, so we have to subtract the area of that overlap once. Since each road is w meters wide, the area of the overlap will be w^2. Thus, we can create the equation:

40w + 60w - w^2 = 291

w^2 - 100w + 291 = 0

(w - 3)(w - 97) = 0

w = 3 or w = 97

Since the width of the crossroads can’t be 97 m (it’s more than either dimension of the park), the width of the crossroads is 3 m.

Answer: B