CPhill

OK.......no prob

What confused you??

Let the granddaughter's age be  "x"

Then, the grandfather's age = "10x"

And the difference in their ages is representsd by

10x - x = 54

So

9x = 54    Divide by 9

x = 6       That's the granddaughter's age

And the grandfather's age is 10x = !0(6) = 60

Nice explanation, Takahiro....Thumbs Up !!!

I'm not sure, but I think the questioner might want to define a "feasible" region here...

It's given by the area inside triangle GHD on the graph...none of the sides are included in the feasible region.......

If this is not the intent........sorry !!!

The Dinosaur may go vegetarian, zegroes, but the Fossil.....Sees.....All......and the Fossil Knows.........All.........

So I'm assuming we have triangle PNM and triangle QPR

So  PN/PM = QP/QR   And

12/17 = 8/QR   And

12*QR = 17*8    So

QR = (17*8/12) = (11+1/3)

Since the ball is a sphere, its surface area is given by

S_A = 4*pi*r²        So we have

531 = 4*pi*r²      Divide on both sides by 4*pi....we have

531/(4*pi) = r²    Take the square root of both sides

r ≈ 6.5 cm

You can use the home page calculator for this.....

If he drove 6 hrs. at 116km/hr., the total length of the trip was 6hrs * 116km = 696km

And he travels 262km in the first 2 hours. So the distance left to travel in the last four hours was :The total distance traveled (696) -  the distance already traveled (262) = 434km

So, the final 4 hrs Bernard traveled 696 - 262 = 434km

And Distance/Time = Rate......... so

      434km/4hrs = 108.5 km/hr

And that's the rate for the rest of the trip.