Josh and Karen live 20 miles apart and at exactly 2 pm, both decide to ride their bikes towards each other's houses so that they can meet on the path somewhere in between. Josh rides at an average speed of 15 miles per hour and Karen rides at an average speed of 10 miles per hour. If Josh takes a 10 minute break after he starts to look at some birds while Karen rides the whole time, how many miles from Karen's house will they meet?

They will meet at a distance 9 miles from Karen's house.

Step-by-step explanation:

Let the distance covered by Josh be and the distance covered by Karen be

The distance between Josh and Karen's houses is 20 miles. That is, the total distance both of them will cover is 20 miles.

Hence,

From the question, if Josh takes a 10 minute break after he starts while Karen rides the whole time, this means

If Karen rides for a total of mins, then Josh would spend mins for the journey

Also, Josh rides at an average speed of 15 miles per hour

and Karen rides at an average speed of 10 miles per hour

Now, for Josh

Distance =

Speed = 15 mile/hour (Covert to mile/minute); (NOTE: 1 hour = 60 mins)

Speed= 0.25 mile/min

Time spent = mins

From

Distance = Speed × Time

Distance = 0.25 mile/min × (t-10) min

= 0.25(t-10) mile

= 0.25t - 2.5

t = ( + 2.5) / 0.25 ....... (1)

For Karen,

Distance =

Speed = 10 mile/hour (Covert to mile/minute);

Speed= mile/min

Time spent = t

Distance = Speed × Time

Then, = mile/min × t min

= mile

t = 6 ......... (2)

Equating equations (1) and (2), we get

( + 2.5) / 0.25 = 6

Then,

( + 2.5) = 1.5

Recall that

Then,

∴ + 2.5 = 1.5

2.5 = 22.5

= 22.5 / 2.5

= 9 miles

This means Karen covers a total distance of 9 miles

Hence, they will meet at a distance 9 miles from Karen's house.

y = 0.77(x)

step-by-step explanation:

the jacket retains this value after 23% cut or retains 77% of original value. plug original 87 jacket price for x and the remaining value should be y.

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.