Question

Two cars A and B start from the same point and travel the same distance. The ratio of their speeds is 3: 4. Car A takes 30 minutes more than car B to complete the journey. If car B takes 't' minutes, then what is the value of 't' (in minutes)?

• A. (60)
• B. (90)
• C. (120)
• D. (150)

Hint:

If speed ratio is (a:b), the corresponding travel time ratio is flipped to (b:a). The units of difference between these ratios is (|b - a|). Here, the difference between parts is (4 - 3 = 1 part). Since 1 part represents 30 minutes, Car B's time ((3 parts)) is simply calculated as: (3 30 = 90 minutes). This mental calculation eliminates algebraic setup steps completely!

Answer 1

The Correct Option is B

Step 1: Recall the link between speed and time.
For a fixed distance, speed and time are inversely related, because distance equals speed times time. If one car is faster, it takes less time for the same road.

Step 2: Set up the inverse ratio.
Speeds are in the ratio $3:4$. So times are in the reverse ratio $4:3$. The slower car A takes the larger share of time.

Step 3: Write the times.
Let car B take $t$ minutes. Then car A, being slower, takes $\frac{4}{3}t$ minutes, since the time ratio is $4:3$.

Step 4: Use the time difference.
Car A takes $30$ minutes more than car B. \[ \frac{4}{3}t - t = 30 \]

Step 5: Simplify the equation.
\[ \frac{4t - 3t}{3} = 30 \quad\Rightarrow\quad \frac{t}{3} = 30 \]

Step 6: Solve for $t$.
Multiply both sides by $3$ to get $t = 90$. So car B takes \[ \boxed{90 \text{ minutes}} \]