The accident took place at 4:09 PM, and Neston measured the angle between the hands of his watch at 4:10 PM.
At 4:00 PM, the angle between the two hands was 120 degrees (1/3 of a circle). The minute hand was moving clockwise at 1/60 of a circle (6 degrees) per minute, decreasing the angle by 60 degrees by 4:10. The hour hand, however, was moving at 1/12 of a circle (30 degrees) per hour; that is, at 1/2 degree per minute, thus increasing the angle by 5 degrees. Therefore, at 4:10, the angle between the two hands was 120 - 60 + 5 = 65 degrees.
Now, suppose that Neston had x pennies. He then had 5x quarters, 10x nickels, and 7x dimes. This makes a total of 23x coins with a total worth of 246x cents.
We thus have 65 (degrees) = 3 * (23x) - (5x - 1) - 69x - 5x + 1 = 64x + 1.
Therefore 64 = 64x and x = 1. The worth of his change is therefore 246 cents, and his mother's age in three years will be 1/6 * 246 = 41. His mother is therefore 38. |
