The distance between logan airport and framingham a car can cover in 20 min. logan express bus can cover this distance in 30 min. how long does it take the car to meet the bus, if the bus moves from framingham to the airport, and the car started from the airport towards framingham simultaneously with the bus?
They will meet in 12 minutes
Let the distance travelled by the car at the point they met be a, then the distance travelled by the bus is x - a.
At the time they met, a/(x/20) = (x - a)/(x/30)
20a/x = 30(x - a)/x
20a = 30x - 30a
50a = 30x
a = 3/5x
Therefore, they met after a/(x/20) = (3/5x)/(x/20) = 12 mins.
∠acb = 8°
∠xba lies on the circle and is half the measure of the intercepted arc ax
measure of arc ax = 2 × 42° = 84°
∠acb is outside the circle and is
∠acb = (arcab - arcax ), hence
∠acb = 0.5 (100 - 84) = 0.5 × 16° = 8°