Question

Two cars left, at $8am$ from the same point, one traveling east at $50mph$ and the other traveling south at $60$mph. At what time will they be $300$ miles apart?

• A. $11:40$am
• B. $11:51$ am
• C. $11:40$ pm
• D. $11:51$ pm

Answer 1

The correct option is B $11:51$ am

The two cars are travelling in directions that are at right angle.

Let $x$ and $y$ be the distances travelled by the two cars in $t$ hours.

Hence, $x=50t$ and $y=60t$

Since the two directions are at right angle, Pythagoras theorem can used to find distance $D$ between the two cars as follows:

$D=\sqrt{x^2+y^2}$

We now find the time at which $D=300$ miles by solving

$\sqrt{x^2+y^2}=300$

Square both sides and substitute $x$ and $y$ by $50t$ and $60t$ respectively to obtain the equation

$(50t{)}^2+(60t{)}^2={300}^2$

Solve the above equations to obtain

$t=3.84$ hours (rounded to two decimal places) or $3$ hours and $51$ minutes (to the nearest minute)

The two cars will $300$ miles apart at

$8+3h{51}^{\prime }=11:51$ am