Raul bikes 6 mi from school at a rate of 3 mi/h. leah leaves school 30 min after raul and bikes the same route at a rate of 4 mi/h. how many hours does it take leah to catch up with raul?

The number of hours it will take Leah to catch up with Raul is equal to 1.5 hour.

Give the following data:

To calculate the number of hours it will take Leah to catch up with Raul;

First of all, we would convert the value of time in minutes to hour:

Conversion:

60 minutes = 1 hour

30 minutes = 0.5 hour

Mathematically, distance with respect to rate and time is given by the formula:

Translating the word problem into an algebraic expression, we have;

For Raul:

For Leah:

Time, t = 1.5 hour

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1.5 h

Explanation:

We know that distance travelled (d) equals rate of travel (r) times time (t) spent in travel. In symbols,

d = rt or rt =d

When Leah starts, Raul is already 30 min (0.5 h) ahead.

So, let t time for Leah and t + 0.5 be the time for Raul.

For Raul: 3(t+0.5) = d

For Leah:         4t = d

When Leah catches up with Raul, both will have travelled the same distance. So,

3(t+0.5) = 4t     Remove parentheses

3t + 1.5 = 4t      Subtract 3t from each side

t = 1.5 h

It takes Leah 1.5 h to catch up with Raul.

Check:

Distance travelled by Raul  = 3 × (1.5 + 0.5) = 3 × 2 = 6 mi

Distance travelled by Leah =                        4 × 1.5 = 6 mi

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