Question

Steven, Mabel, Sofia, and Finn went on a very long trip to visit their grandfather, Max. They rode a taxi which ran a distance of 40 km within 2 hours after they left the house. During their travel, Mabel received a call from their grand uncle, Ford. His taxi had a flat wheel and asked them to pick him up. They picked him up half an hour later and resumed their way. After an hour, their taxi could not enter the woods where their grandfather lives, so, they decided all together to walk. 50 km, and 10 hours later, they reached Max’s cabin in the woods.

Plot and determine the slope of the curve. (20 points)

Find the distance Steven, Mabel, Sofia, and Finn found Ford during the trip, and the distance where they started to walk.

Answer 1

$\text{Let }AD- \text{traveler movement by car }$

$\text{point B -call from uncle Ford }$

$AB_y -\text{distance traveled or projection on an axis Y}$

$AB_y = 40km$

$t_{AB}= 2h$

$\text{taxi speed :}$

$v_{tx}=\frac{AB_y}{t_{AB}}= \frac{40}{2}=20\frac{km}{h}$

$\text{point C -uncle Ford meeting :}$

$t_{AC}= t_{AB}+0.5=2.5h$

$AC_y = v_{tx}t_{AC}= 2.5*20= 50km$

$\text{point D -end of taxi ride :}$

$t_{AВ}= t_{AС}+1=3.5h$

$AD_y = v_{tx}t_{AD}= 2.5*20= 70km$

$\text{the tangent of the slope of a straight line with uniform motion }$

$\text{is numerically equal to the speed}$

$\tan(AD) =20$

$\tan(DE) =\frac{DE_y}{h_{DE}}=\frac{50}{10}= 5$

$\text{Answer:}$

$\text{angle of inclination of straight lines }$

$\tan(AD) =20$

$\tan(DE)= 5$

$\text{uncle Ford meeting distance :}AC_y = 50km$

$\text{distance where they started to walk.}AD_y = 70km$