Answer:
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.
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Check:
Distance travelled by Raul = 3 × (1.5 + 0.5) = 3 × 2 = 6 mi
Distance travelled by Leah = 4 × 1.5 = 6 mi
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:
[tex]Distance = rate \times time[/tex]
Translating the word problem into an algebraic expression, we have;
For Raul:
[tex]3(t+0.5) = 6[/tex]
For Leah:
[tex]4t = 6\\\\t=\frac{6}{4}[/tex]
Time, t = 1.5 hour
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