C leaves home going 40 km/h. when c is 9 km from home, d starts after c from the same place, going 58 km/h. how long does it take d to catch up to c?
time c goes alone = 9/40
time d goes = (t -9/40)
distances are the same so
40 t = 58 (t - 9/40)
To find out how long it takes for D to catch up to C, we need to calculate the time it takes for D to cover the distance between them.
Let's assume t is the time it takes for D to catch up to C.
Given:
- C's speed is 40 km/h
- D's speed is 58 km/h
Since C starts 9 km ahead of D, we can say that the distance D needs to cover is 9 km less than the total distance between them.
The relative speed of D catching up to C is the difference in their speeds, which is 58 km/h - 40 km/h = 18 km/h.
Using the formula: Distance = Speed * Time, we can find the equation for each person's distance covered:
Distance covered by C = 40 km/h * t
Distance covered by D = 18 km/h * t
Since D starts 9 km behind C, we have the equation:
Distance covered by C - Distance covered by D = 9 km
(40 km/h * t) - (18 km/h * t) = 9 km
Simplifying the equation:
22 km/h * t = 9 km
Dividing both sides by 22 km/h:
t = 9 km / 22 km/h
Now we can find the value of t by dividing the distance by the speed:
t ≈ 0.41 hours (rounded to two decimal places)
Therefore, it takes approximately 0.41 hours (or 24.6 minutes) for D to catch up to C.