Question

A plane left $30$ minutes later then the scheduled time and in order to reach the destination $1500km$ away in time, it had to increase the speed by $250km/h$ from the usual speed. Find its usual speed.

• A. $720km/h$
• B. $740km/h$
• C. $730km/h$
• D. $750km/h$

Answer 1

The correct option is D $750km/h$

Distance is 1500 km

Since the plane left 30 min early

$\therefore$ To cover the same dist in same time it will take $(t-\frac{30}{60})$ hours & speed is increased by 250km/h

$\therefore x+250$

we know $xt=1500$ $\to$Distance

$\downarrow$ $\downarrow$

used speed usual time

$(t-\frac{1}{2})(x+250)=1500$

$xt+250t-\frac{1}{2}x-125=1500$

$250\times \frac{1500}{x}-\frac{1}{2}x-125$

$250t-\frac{1500}{2t}-125=0$

$10t-\frac{30}{t}-5=0$

$10t^2-30-5t=0$

${10t}^2-5t-30=0$

${10t}^2-20t+15t-30=0$

$10t(t-2)+15(t-2)=0$

$(10t+15)(t-2)=0$

$t=2$ hours

$x=750$km/h