Quadratics Distance-Speed-Time Rate Word Problem A small plane is

Landin Harmon

Landin Harmon

Answered question

2022-03-31

Quadratics Distance-Speed-Time Rate Word Problem
A small plane is travelling between Windsor and Pelee Island (a distance of approx. 60 km) and is directly affected by the prevailing winds. Thus, the actual speed of the plane with respect to the ground is the speed of the plane (160 km/h) plus or minus the wind speed, w. Develop a simplified equation for the total time it takes to make a round trip if the wind speed is w.

Answer & Explanation

Cassius Villarreal

Cassius Villarreal

Beginner2022-04-01Added 11 answers

Step 1
=60160+w+60160w=60(160w)+60(160+w)(160+w)(160w)
=960060w+9600+60w(160+w)(160w)=19200(160+w)(160w)
=1920025600+160w160ww2=1920025600w2
Step 2
For this scenario of finding round trip time where you have 2 islands, your wind direction is always parallel to your flight path, and the wind is always in the same direction you could reduce it to this formula.
r= rate (in this instance 160 km/h) w= wind speed (assuming here is in units km/h) d=km between the 2 islands
T=d(rw)+d(r+w)(r+w)(rw)=dr+drr2w2=2drr2w2
If we take the problem with no wind.
r=160kmh w= wind speed (assuming here is in units km/h) d=60km.(2)(60)(160)160202=1920025600=34 of an hour
Problem with 30 km/h wind speed r=160kmh w=30kmh d=60km (2)(60)(160)1602302=1920025600900=1920024700=192247 of an hour =∼0.777 of an hour.

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