Question

On a sunny day, Liam decided to walk 15 mi to his grandmother's house. After walking for a while at a rate of 3 mph, Liam realized that it might start raining, so he decided to take a taxi the rest of the way. The taxi traveled at a speed of 30 mph. If he arrived at his grandmother's house 2 hours after he started, what distance did Liam travel by taxi?

a) 30 mi
b) 45 mi
c) 60 mi
d) 75 mi

Answer 1

Liam traveled 48 miles by taxi.

Step-by-step explanation:

To find the distance Liam traveled by taxi, we need to first calculate how long he walked. We can use the formula distance = rate × time to calculate the time Liam spent walking. Given that Liam walked for a while at a rate of 3 mph, and his total travel time was 2 hours, we can set up the equation 3t + t = 2, where t is the time Liam spent walking. Solving for t, we get t = 0.4 hours.

Since the total travel time is 2 hours and Liam walked for 0.4 hours, the time spent in the taxi is 2 - 0.4 = 1.6 hours.

Now, we can find the distance Liam traveled by taxi by multiplying the taxi's speed of 30 mph by the time spent in the taxi: distance = rate × time = 30 mph × 1.6 hours = 48 miles.

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