Two children own two-way radios that have a maximum range of 2 miles. One leaves a certain point at 1:00 P.M., walking due north at a rate of 4 . The other leaves the same point at 1:15 P.M., traveling due south at 6 . When will they be unable to communicate with one another?

Brittney Lord 2021-01-15 Answered
Two children own two-way radios that have a maximum range of 2 miles. One leaves a certain point at 1:00 P.M., walking due north at a rate of 4 . The other leaves the same point at 1:15 P.M., traveling due south at 6 . When will they be unable to communicate with one another?
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Expert Answer

Sadie Eaton
Answered 2021-01-16 Author has 104 answers
Step 1 Consider that the maximum range of the radio is 2 miles. One leaves at 1:00 P.M with rate 4 miles/hr due north and other leaves at 1:15 P.M with rate eaves at 1:00 P.M with rate 4 miles/hr due south. Find at what time they will be unable to communicate. Let t denote the time in hour. after 1:00 P.M. Since 60 minutes =1 hour therefore, 15minutes=604minutes=14hour Step 2 SinceDistance=Speedtime Distance travelled by first children (d1) at any time t after 1:00 P.M will be 4t and distance travelled by second children (d2) at any time t after 1:00 P.M will be d2={00t146(t14)t14 Children will unable to communicate when the distance between them will be greater than 2 miles and since they are travelling in opposite direction therefore the distance between them will be the sum of the distance they have travelled. For 0t14 the distance between the is maximum 414=1 mile which is less than 2 mile hence they will be able to communicate. After t14 they will be unable to communicate when distance between them will be greater than 2 that is, 4t+6(t14)>2
10t32>2
10t>72
t>720hour and 720hr=72060 minutes
=21 minutes Hence 21 minutes after 1:00 P.M that is after 1:21 P.M they will be unable to communicate.
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