Pergunta

A plane flies 435 miles with the wind and 375 miles against the wind in the same length of time.If the speed of the wind is 10 mph, find the speed of the plane in still air. The speed of the plane in still air is square mph.
Solução

4.1232 Voting

ThiagoMestre · Tutor por 5 anos
Responder
To solve this problem, we need to use the concept of relative speed.<br /><br />Let's denote the speed of the plane in still air as \( v \) mph.<br /><br />When the plane flies with the wind, the effective speed of the plane is \( v + 10 \) mph.<br />When the plane flies against the wind, the effective speed of the plane is \( v - 10 \) mph.<br /><br />Since the plane flies the same distance with and against the wind, and the time taken is the same, we can set up the following equation:<br /><br />\[<br />\frac{435}{v + 10} = \frac{375}{v - 10}<br />\]<br /><br />To solve this equation, we can cross-multiply:<br /><br />\[<br />435(v - 10) = 375(v + 10)<br />\]<br /><br />Expanding both sides:<br /><br />\[<br />435v - 4350 = 375v + 3750<br />\]<br /><br />Combining like terms:<br /><br />\[<br />435v - 375v = 3750 + 4350<br />\]<br /><br />\[<br />60v = 8100<br />\]<br /><br />Dividing both sides by 60:<br /><br />\[<br />v = 135<br />\]<br /><br />Therefore, the speed of the plane in still air is \( 135 \) mph.
Clique para avaliar: