On average, Sherry can travel four times as fast on cross-country skis as she can with snowshoes. To travel 24 km, she needs 6 h more if she is snowshoeing than if she is skiing. What is her average speed on crosscountry skis?
Answer:
Sherry speed on crosscountry skis is 12 km/hr
Solution:
Let "n" be the Sherry's rate on snowshoes
Given that,
Sherry can travel four times as fast on cross-country skis as she can with snowshoes
Sherry rate on cross country skis = 4n
Distance to be traveled = 24 km
Time is given by formula:
[tex]time = \frac{distance}{speed}[/tex]
She needs 6 h more if she is snowshoeing than if she is skiing
Therefore, we get
time taken by snowshoes - 6 = time taken on country skis
[tex]\frac{24}{n} - 6 = \frac{24}{4n}[/tex]'
[tex]\frac{24-6n}{n} = \frac{24}{4n}\\\\24 - 6n = 6\\\\6n = 24 - 6\\\\6n = 18\\\\n = 3[/tex]
Thus her speed in snowshoes is 3 km/hr
Speed in country skis = 4n = 4 x 3 = 12 km/hr
Thus speed in country skis is 12 km/hr
