Some problems I can't solve

N:Dure wrote:??

1) Distance is same both ways, speeds are constant, therefore we can calculate the average speed using the formula -
2S1*S2/S1+S2
Lexy's average speed = 2*5*15/5+15 = 7.5

Ben's speed = 7.5/2
Time spent = Distance / speed = 5+5 / 7.5/2 = 10*2/7.5 = 20*2/15 hrs.
In minutes = (20*2/15)*60 = 160 minutes. Option D.

2) angle CAB = 45, angle COB = 2 * angle CAB = 2*45 = 90.
Area of sector covered by COB = 90/360(pie*r^2) = 1/4(pie)*2^2 = pie ......... (1)

Shaded region = area of sector covered by sector + area of triangle COA.
area of triangle can be calculated as = 1/2*(b*h) ; base and height are both 2.
THerefore are of triangle = (1/2)*2*2 = 2...........................................................(2)
Area of shaded region = (1)+(2) = pie + 2. Option B.

3) x^2-y^2 = 12; x^2-y^2 = (x-y)(x+y) = 12; x+y=3; using x+y; (3)(x-y)=12. Therefore x-y = 4.
Option D.

beat_gmat_09 wrote:

N:Dure wrote:??

1) Distance is same both ways, speeds are constant, therefore we can calculate the average speed using the formula -
2S1*S2/S1+S2
Lexy's average speed = 2*5*15/5+15 = 7.5

Ben's speed = 7.5/2
Time spent = Distance / speed = 5+5 / 7.5/2 = 10*2/7.5 = 20*2/15 hrs.
In minutes = (20*2/15)*60 = 160 minutes. Option D.

2) angle CAB = 45, angle COB = 2 * angle CAB = 2*45 = 90.
Area of sector covered by COB = 90/360(pie*r^2) = 1/4(pie)*2^2 = pie ......... (1)

Shaded region = area of sector covered by sector + area of triangle COA.
area of triangle can be calculated as = 1/2*(b*h) ; base and height are both 2.
THerefore are of triangle = (1/2)*2*2 = 2...........................................................(2)
Area of shaded region = (1)+(2) = pie + 2. Option B.

3) x^2-y^2 = 12; x^2-y^2 = (x-y)(x+y) = 12; x+y=3; using x+y; (3)(x-y)=12. Therefore x-y = 4.
Option D.

good solutions methods.
In Q1, If Ben walks at half the speed, he takes twice as long to cover the same distance. find Lexy's time and multiply times two: Lexy takes one hour to do 5 miles, then 1/3 of an hour to do 5 miles at 15 mph - total time of 4/3. So Ben's time is twice that, or 8/3 = 2 hours and 2/3 = 120+40 minutes = 160.