MATH SOLVE

4 months ago

Q:
# A DC10 airplane travels 3000 km with a tailwind in 3 hr. It travels 3000 km with a headwind in 4 hr. Find the speed of the plane and the speed of the wind. Use substitution or elimination to solve.

Accepted Solution

A:

Answer:The speed of plane is 875 km/h and speed of wind is 125 km/hr
Explanation:
Assuming v the speed of plane and w the speed of wind
Then, the overall speed will be given as (v+w)
The speed is calculated by the formula; [tex]$\frac{\text { Distance }}{\text { Time }}$[/tex]For tailwind, given distance travelled is 3000 km in 3 hrs
Putting the values in the formula;
(v+w) = [tex]$\frac{3000}{3}$[/tex] (v+w) = 1000 ……eqn (1)
Similarly, for headwind, given distance travelled is 3000 km in 4 hrs
(v-w) = [tex]$\frac{3000}{4}$[/tex] (v-w) = 750 ……eqn (2)
Adding (1) and (2), we get
2v = 1750
v = 875 km/hr
putting value in eqn (1), we get: w = 125 km/hr
Therefore, the speed of plane is 875 km/h and speed of wind is 125 km/hr.