Maya drove at an average speed of 30 miles per hour for some time
and then at an average speed of 60 miles per hour for the rest of the
journey. If she made no stops during the trip and her average speed
for the entire journey was 48 miles per hour, for what fraction of the
total time did she drive at an average speed of 30 miles/hour?
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Given:
v1 = 30 miles/hr
v2 = 60 miles/hr
v = 48 miles/hr
To Find:
The fraction of the total time for which she drives at an average speed of 30 miles/hour.
Calculation:
- Let the time for v1 and v2 speeds be t1 and t2 respectively.
- Then according to the question:
v = (v1 t1 + v2 t2)/ (t1 + t2)
⇒ 48 = 30t1 + 60 t2)/ (t1 + t2)
⇒ 48 t1 + 48 t2 = 30 t1 + 60 t2
⇒ (48-30) t1 = (60-48) t2
⇒ 18 t1 = 12 t2
⇒ t1 = 2 t2 / 3
- Fraction of t1 = t1/(t1+t2)
⇒ Fraction of t1 = (2 t2/3) / (2 t2/3+t2)
⇒ Fraction of t1 = (2 t2/3)/(5 t2/3)
⇒ Fraction of t1 = 2/5
- So, the fraction of the total time for which she drives at an average speed of 30 miles/hour is Two-Fifth (2/5).
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