Question

The distance travelled by a state run train is defined by the function D(t)=8t+5t^2 after t hours where D is in miles. what is the distance travelled in the 3rd hour in miles?

Answer 1

Distance travelled in the 3rd hour = Distance travelled in first 3 hours - Distance travelled in first 2 hours
⇒ Distance travelled in the 3rd hour = D(3) - D(2)

D(t) = 8t + 5t²
D(3) = 8×3 + 5×3² = 24 + 45 = 69 miles
D(2) = 8×2 + 5×2² = 16 + 20 = 36 miles

Distance travelled in the 3rd hour = 69-36 = 33 miles