Question

Jim drives 40 mph to his mother's house and 20 mph on the way back. Show that his average speed for the trip is 26 and 2/3mph regardless of the distance to his mother's house

Answer 1

Answer:

$Given : Jim travels the first 3 hours of his journey at 60 mph speed and the remaining 5 hours at 24 mph speed.</p><p></p><p>Need To Find : Average Speed of Jim's travel in mph .</p><p></p><p>⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀</p><p></p><p>⠀⠀⠀⠀Finding Distance Travelled in both case of speed : </p><p></p><p>⠀Finding Distance Travelled in first 3 hrs at the speed of 60 mph : </p><p></p><p>[tex]\dag\:\:\it{ As,\:We\:know\:that\::}$

$\qquad \dag\:\:\bigg\lgroup \sf{ Distance \:: Speed \times Time }\bigg\rgroup$

⠀⠀⠀⠀Here , Speed is 60 mph & Time is 3 hrs .

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}$

$\qquad \longmapsto \sf{ Distance = 60 \times 3 }$

$\qquad \longmapsto \frak{\underline{\purple{\:Distance = 180km }} }$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {\:Distance \:Travelled \:in\:first\:3\:hours \:is\:\bf{180\: km}}}}$

⠀Finding Distance Travelled in remaining 5 hrs at the speed of 24 mph :

$\dag\:\:\it{ As,\:We\:know\:that\::}$

$\qquad \dag\:\:\bigg\lgroup \sf{ Distance \:: Speed \times Time }\bigg\rgroup$

⠀⠀⠀⠀Here , Speed is 24 mph & Time is 5 hrs .

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}$

$\qquad \longmapsto \sf{ Distance = 24 \times 5 }$

$\qquad \longmapsto \frak{\underline{\purple{\:Distance = 120 km }} }$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {\:Distance \:Travelled \:in\:remaining \:8\:hours \:is\:\bf{120\: km}}}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

⠀⠀⠀⠀Now , Finding Average Speed :

$\dag\:\:\it{ As,\:We\:know\:that\::}$

$\qquad \dag\:\:\bigg\lgroup \sf{ Average \:Speed\:\:: \dfrac{Total\;Distance \:Travelled\:}{Total\:Time\:Taken}}\bigg\rgroup$

Here ,

⠀⠀⠀⠀Total Distance Travelled = Distance Travelled in first 3 hrs + Distance Travelled ⠀⠀⠀⠀in remaining 5 hrs .

⠀⠀⠀⠀Total Distance Travelled = 120 km + 180 km

⠀⠀⠀⠀Total Distance Covered in journey = 300 km .

⠀⠀&

⠀⠀⠀⠀Total Time Taken = 3hrs + 5 hrs

⠀⠀⠀⠀Total Time Taken = 8 hrs .

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}$

$\qquad \longmapsto \sf { Average \:Speed = \dfrac{300}{8}}$

$\qquad \longmapsto \sf { Average \:Speed = \cancel {\dfrac{300}{8}}}$

$\qquad \longmapsto \frak{\underline{\purple{\:Average \:Spped\: = 37.5 mph }} }$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {\:The\:Average \:Speed\:of\:Jim's\:travel \:is\:\bf{37.5\:mph}}}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀[/tex]